{"id":7104,"date":"2025-08-08T05:39:31","date_gmt":"2025-08-08T05:39:31","guid":{"rendered":"https:\/\/tutorschool.in\/?p=7104"},"modified":"2025-08-11T10:06:00","modified_gmt":"2025-08-11T10:06:00","slug":"class-10-maths-ncert-chapter-2-polynomials-solutions-2","status":"publish","type":"post","link":"https:\/\/tutorschool.in\/blog\/class-10-maths-ncert-chapter-2-polynomials-solutions-2\/","title":{"rendered":"Class 10 Maths NCERT Chapter 2 (Polynomials) Solutions"},"content":{"rendered":"<h2>Summary (What we have discussed)<\/h2>\n<p>Hello! Are you using the NCERT textbook to study Class 10 Maths Chapter 1: &#8220;<strong>Real Numbers<\/strong>&#8220;? The <strong>Fundamental Theorem of Arithmetic<\/strong>, <strong>Euclid&#8217;s Division Lemma<\/strong>, and the distinction between <strong>rational and irrational numbers<\/strong> are just a few of the fascinating questions that are covered in this page.<\/p>\n<p>During your studies, you will discover things such as:<\/p>\n<ul>\n<li>How to determine a number&#8217;s <strong>LCM<\/strong> (Least Common Multiple) and <strong>HCF<\/strong> (Highest Common Factor).<\/li>\n<li>How to demonstrate why certain numbers, such as \u221a2 and \u221a3, are <strong>irrational<\/strong>.<\/li>\n<li>How to determine if a <strong>decimal<\/strong> is non-terminating or terminating.<\/li>\n<\/ul>\n<p>\t\t\t\t\t<button id=\"e-n-tab-title-1191938011\" aria-selected=\"true\" data-tab-index=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"e-n-tab-content-1191938011\" style=\"--n-tabs-title-order: 1;\"><br \/>\n\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M352 96c0-53.02-42.98-96-96-96s-96 42.98-96 96 42.98 96 96 96 96-42.98 96-96zM233.59 241.1c-59.33-36.32-155.43-46.3-203.79-49.05C13.55 191.13 0 203.51 0 219.14v222.8c0 14.33 11.59 26.28 26.49 27.05 43.66 2.29 131.99 10.68 193.04 41.43 9.37 4.72 20.48-1.71 20.48-11.87V252.56c-.01-4.67-2.32-8.95-6.42-11.46zm248.61-49.05c-48.35 2.74-144.46 12.73-203.78 49.05-4.1 2.51-6.41 6.96-6.41 11.63v245.79c0 10.19 11.14 16.63 20.54 11.9 61.04-30.72 149.32-39.11 192.97-41.4 14.9-.78 26.49-12.73 26.49-27.06V219.14c-.01-15.63-13.56-28.01-29.81-27.09z\"><\/path><\/svg>\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M352 96c0-53.02-42.98-96-96-96s-96 42.98-96 96 42.98 96 96 96 96-42.98 96-96zM233.59 241.1c-59.33-36.32-155.43-46.3-203.79-49.05C13.55 191.13 0 203.51 0 219.14v222.8c0 14.33 11.59 26.28 26.49 27.05 43.66 2.29 131.99 10.68 193.04 41.43 9.37 4.72 20.48-1.71 20.48-11.87V252.56c-.01-4.67-2.32-8.95-6.42-11.46zm248.61-49.05c-48.35 2.74-144.46 12.73-203.78 49.05-4.1 2.51-6.41 6.96-6.41 11.63v245.79c0 10.19 11.14 16.63 20.54 11.9 61.04-30.72 149.32-39.11 192.97-41.4 14.9-.78 26.49-12.73 26.49-27.06V219.14c-.01-15.63-13.56-28.01-29.81-27.09z\"><\/path><\/svg><br \/>\n\t\t\t\tLong Answer Type Questions<br \/>\n\t\t<\/button><\/p>\n<table>\n<tbody>\n<tr>\n<td>Class 10<\/td>\n<td>MATHS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Chapter<\/td>\n<td>POLYNOMIALS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>NCERT MATHS (ENGLISH)<\/td>\n<td>Long Answer Type Questions<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Medium<\/td>\n<td>English<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Academic Year<\/td>\n<td>2023-2024<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><strong>Question 1<\/strong><\/p>\n<p>lf -3 is one of the zeroes of the polynomial (k\u22121)x<sup>2<\/sup>+kx+1, find the value of k.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques1\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 2<\/strong><\/p>\n<p>A quadratic polynomial, whose zeroes are-3 and 4, is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques2\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 3<\/strong><\/p>\n<p>If the zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+(a+1)x+b\u00a0are 2 and -3, then find the values of a and b<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques3\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 4<\/strong><\/p>\n<p>The number of polynomials having zeroes as -2 and 5 is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques4\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 5<\/strong><\/p>\n<p>If one of the zeroes of the cubic polynomial\u00a0ax<sup>3<\/sup>+bx<sup>2<\/sup>+cx+d\u00a0is zero, then the product of other two zeroes is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques5\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 6<\/strong><\/p>\n<p>If one of the zeroes of the cubic polynomial\u00a0x<sup>3<\/sup>+ax<sup>2<\/sup>+bx+c\u00a0is\u00a0\u22121,then find the product of other two zeroes.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques6\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 7<\/strong><\/p>\n<p>The zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+99x+127\u00a0are<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques7\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 8<\/strong><\/p>\n<p>The zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+kx+k\u00a0where\u00a0k\u22600, are : (1)cannot both be positive (2)cannot both be negative (3)are always unequal (4)are always equal<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques8\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 9<\/strong><\/p>\n<p>If the zeroes of the quadratic polynomial\u00a0ax<sup>2<\/sup>+bx+c, where\u00a0c\u22600, are equal, then<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques9\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 10<\/strong><\/p>\n<p>If one of the zeroes of a quadratic polynomial of the form\u00a0x<sup>2<\/sup>+ax+b\u00a0is the negative of the other, then it<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques10\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 11<\/strong><\/p>\n<p>Which of the following is not the graph of a quadratic polynomial?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques11\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 12<\/strong><\/p>\n<p>Answer the following and justify.<br \/>(i) can\u00a0x<sup>2<\/sup>\u22121\u00a0be the quotient on division of\u00a0x<sup>6<\/sup>+2x<sup>3<\/sup>+x\u22121\u00a0by a polynomial in x of degree 5?<br \/>(ii) What will the quotient and remainder be on division of\u00a0ax<sup>2<\/sup>+bx+c\u00a0by\u00a0px<sup>3<\/sup>+qx<sup>2<\/sup>+rx+s,p\u22600?<br \/>(iii) If on division of a polynomial\u00a0p(x)\u00a0by a polynomial\u00a0g(x), the quotient is zero, what is the relation between the degree of\u00a0p(x)\u00a0and\u00a0g(x)?<br \/>(iv) If on division of a non-zero polynomial\u00a0p(x)\u00a0by a polynomial\u00a0g(x), the remainder is zero, what is the relation between the degrees of\u00a0p(x)\u00a0and\u00a0g(x)?<br \/>(v) Can the quadratic polynomial\u00a0x<sup>2<\/sup>+kx+k\u00a0have equal zeroes for some odd integer\u00a0k&gt;1?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques12\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 13<\/strong><\/p>\n<p>Are the following statements &#8216;True&#8217; or &#8216;False&#8217;? Justify your answer.<br \/>(i) If the zeroes of a quadratic polynomial\u00a0ax<sup>2<\/sup>+bx+c\u00a0are both positive, then a,b and c all have the same sign.<br \/>(ii) If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial.<br \/>(iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not ve a quadratic polynomial.<br \/>(iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.<br \/>(v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.<br \/>(vi) If all three zeroes of a cubic polynomial\u00a0x<sup>3<\/sup>+ax<sup>2<\/sup>\u2212bx+c\u00a0are positive, then atleast one of a,b and c is non-negative.<br \/>(vii) The only value of k for which the quadratic polynomial\u00a0kx<sup>2<\/sup>+x+k\u00a0has equal zeroes is\u00a01\/2.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques13\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 14<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(i)\u00a04x<sup>2<\/sup>\u22123x\u22121<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques14\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 15<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(ii)\u00a03x<sup>2<\/sup>+4x\u22124<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques15\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 16<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(iii)\u00a05t<sup>2<\/sup>+12t+7.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques16\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 17<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (iv)\u00a0t<sup>3<\/sup>\u22122t<sup>2<\/sup>\u221215t.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques17\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 18<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(v)\u00a02x<sup>2<\/sup>+(7\/2)x+3\/4<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques18\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 19<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (vi)\u00a04x<sup>2<\/sup>+5\u221a2x\u22123.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques19\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 20<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(vii)\u00a02s<sup>2<\/sup>\u2212(1+2\u221a2)s+\u221a2<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques20\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 21<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(viii)\u00a0v<sup>2<\/sup>+4\u221a3v\u221215<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques21\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 22<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(ix)\u00a0y<sup>2<\/sup>+(3\u221a5\/2)y\u22125<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques22\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 23<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(x)\u00a07y<sup>2<\/sup>\u2212(11\/3)y\u22122\/3<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques23\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 24<\/strong><\/p>\n<p>For each of the following find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorisation. (i)\u00a0\u22128\/3,4\/3\u00a0(ii)\u00a0\u22123\/2\u221a5,\u22121\/2<\/p>\n<p>\t\t\t\t\t<a href=\"#\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 25<\/strong><\/p>\n<p>Given that zeroes of cubic polynomial\u00a0x<sup>3<\/sup>\u22126x<sup>2<\/sup>+3x+10\u00a0are of the form a,a+b,a+2b for some real numbers a and b, find the values of a and b as well as zeroes of the given polynomial.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques25\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 26<\/strong><\/p>\n<p>If\u00a0\u221a2\u00a0is a zero of\u00a0p(x)=6x<sup>3<\/sup>+\u221a2x<sup>2<\/sup>\u221210x\u22124\u221a2,\u00a0find the remaining zeros<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques26\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 27<\/strong><\/p>\n<p>The value of\u00a0k, if\u00a0x<sup>2<\/sup>+2x+k\u00a0is a factor of\u00a02x<sup>4<\/sup>+x<sup>3<\/sup>\u221214x<sup>2<\/sup>+5x+6\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques27\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 28<\/strong><\/p>\n<p>If\u00a0x\u2212\u221a5\u00a0is a factor of the cubic polynomial\u00a0x<sup>3<\/sup>\u22123\u221a5x<sup>2<\/sup>+13x\u22123\u221a5, then find all the zeroes of the polynomial.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques28\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 29<\/strong><\/p>\n<p>For which values of\u00a0a\u00a0and\u00a0b, the zeroes of\u00a0q(x)=x<sup>3<\/sup>+2x<sup>2<\/sup>+a\u00a0are also the zeroes of the polynomial\u00a0p(x)=x<sup>5<\/sup>\u2212x<sup>4<\/sup>\u22124x<sup>3<\/sup>+3x<sup>2<\/sup>+3x+b? Which zeores of\u00a0p(x)\u00a0are not the zeroes of\u00a0q(x)?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques29\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<table>\n<tbody>\n<tr>\n<td>Class 10<\/td>\n<td>MATHS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Chapter<\/td>\n<td>POLYNOMIALS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>NCERT MATHS (ENGLISH)<\/td>\n<td>Long Answer Type Questions<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Medium<\/td>\n<td>English<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Academic Year<\/td>\n<td>2023-2024<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<p><strong>Question 1<\/strong><\/p>\n<p>lf -3 is one of the zeroes of the polynomial (k\u22121)x<sup>2<\/sup>+kx+1, find the value of k.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques1\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 2<\/strong><\/p>\n<p>A quadratic polynomial, whose zeroes are-3 and 4, is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques2\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 3<\/strong><\/p>\n<p>If the zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+(a+1)x+b\u00a0are 2 and -3, then find the values of a and b<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques3\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 4<\/strong><\/p>\n<p>The number of polynomials having zeroes as -2 and 5 is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques4\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 5<\/strong><\/p>\n<p>If one of the zeroes of the cubic polynomial\u00a0ax<sup>3<\/sup>+bx<sup>2<\/sup>+cx+d\u00a0is zero, then the product of other two zeroes is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques5\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 6<\/strong><\/p>\n<p>If one of the zeroes of the cubic polynomial\u00a0x<sup>3<\/sup>+ax<sup>2<\/sup>+bx+c\u00a0is\u00a0\u22121,then find the product of other two zeroes.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques6\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 7<\/strong><\/p>\n<p>The zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+99x+127\u00a0are<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques7\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 8<\/strong><\/p>\n<p>The zeroes of the quadratic polynomial\u00a0x<sup>2<\/sup>+kx+k\u00a0where\u00a0k\u22600, are : (1)cannot both be positive (2)cannot both be negative (3)are always unequal (4)are always equal<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques8\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 9<\/strong><\/p>\n<p>If the zeroes of the quadratic polynomial\u00a0ax<sup>2<\/sup>+bx+c, where\u00a0c\u22600, are equal, then<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques9\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 10<\/strong><\/p>\n<p>If one of the zeroes of a quadratic polynomial of the form\u00a0x<sup>2<\/sup>+ax+b\u00a0is the negative of the other, then it<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques10\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 11<\/strong><\/p>\n<p>Which of the following is not the graph of a quadratic polynomial?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques11\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 12<\/strong><\/p>\n<p>Answer the following and justify.<br \/>(i) can\u00a0x<sup>2<\/sup>\u22121\u00a0be the quotient on division of\u00a0x<sup>6<\/sup>+2x<sup>3<\/sup>+x\u22121\u00a0by a polynomial in x of degree 5?<br \/>(ii) What will the quotient and remainder be on division of\u00a0ax<sup>2<\/sup>+bx+c\u00a0by\u00a0px<sup>3<\/sup>+qx<sup>2<\/sup>+rx+s,p\u22600?<br \/>(iii) If on division of a polynomial\u00a0p(x)\u00a0by a polynomial\u00a0g(x), the quotient is zero, what is the relation between the degree of\u00a0p(x)\u00a0and\u00a0g(x)?<br \/>(iv) If on division of a non-zero polynomial\u00a0p(x)\u00a0by a polynomial\u00a0g(x), the remainder is zero, what is the relation between the degrees of\u00a0p(x)\u00a0and\u00a0g(x)?<br \/>(v) Can the quadratic polynomial\u00a0x<sup>2<\/sup>+kx+k\u00a0have equal zeroes for some odd integer\u00a0k&gt;1?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques12\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 13<\/strong><\/p>\n<p>Are the following statements &#8216;True&#8217; or &#8216;False&#8217;? Justify your answer.<br \/>(i) If the zeroes of a quadratic polynomial\u00a0ax<sup>2<\/sup>+bx+c\u00a0are both positive, then a,b and c all have the same sign.<br \/>(ii) If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial.<br \/>(iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not ve a quadratic polynomial.<br \/>(iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.<br \/>(v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.<br \/>(vi) If all three zeroes of a cubic polynomial\u00a0x<sup>3<\/sup>+ax<sup>2<\/sup>\u2212bx+c\u00a0are positive, then atleast one of a,b and c is non-negative.<br \/>(vii) The only value of k for which the quadratic polynomial\u00a0kx<sup>2<\/sup>+x+k\u00a0has equal zeroes is\u00a01\/2.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques13\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 14<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(i)\u00a04x<sup>2<\/sup>\u22123x\u22121<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques14\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 15<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(ii)\u00a03x<sup>2<\/sup>+4x\u22124<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques15\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 16<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(iii)\u00a05t<sup>2<\/sup>+12t+7.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques16\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 17<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (iv)\u00a0t<sup>3<\/sup>\u22122t<sup>2<\/sup>\u221215t.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques17\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 18<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(v)\u00a02x<sup>2<\/sup>+(7\/2)x+3\/4<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques18\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 19<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials (vi)\u00a04x<sup>2<\/sup>+5\u221a2x\u22123.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques19\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 20<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(vii)\u00a02s<sup>2<\/sup>\u2212(1+2\u221a2)s+\u221a2<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques20\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 21<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(viii)\u00a0v<sup>2<\/sup>+4\u221a3v\u221215<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques21\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 22<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(ix)\u00a0y<sup>2<\/sup>+(3\u221a5\/2)y\u22125<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques22\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 23<\/strong><\/p>\n<p>Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials<br \/>(x)\u00a07y<sup>2<\/sup>\u2212(11\/3)y\u22122\/3<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques23\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 24<\/strong><\/p>\n<p>For each of the following find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorisation. (i)\u00a0\u22128\/3,4\/3\u00a0(ii)\u00a0\u22123\/2\u221a5,\u22121\/2<\/p>\n<p>\t\t\t\t\t<a href=\"#\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 25<\/strong><\/p>\n<p>Given that zeroes of cubic polynomial\u00a0x<sup>3<\/sup>\u22126x<sup>2<\/sup>+3x+10\u00a0are of the form a,a+b,a+2b for some real numbers a and b, find the values of a and b as well as zeroes of the given polynomial.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques25\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 26<\/strong><\/p>\n<p>If\u00a0\u221a2\u00a0is a zero of\u00a0p(x)=6x<sup>3<\/sup>+\u221a2x<sup>2<\/sup>\u221210x\u22124\u221a2,\u00a0find the remaining zeros<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques26\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 27<\/strong><\/p>\n<p>The value of\u00a0k, if\u00a0x<sup>2<\/sup>+2x+k\u00a0is a factor of\u00a02x<sup>4<\/sup>+x<sup>3<\/sup>\u221214x<sup>2<\/sup>+5x+6\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques27\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 28<\/strong><\/p>\n<p>If\u00a0x\u2212\u221a5\u00a0is a factor of the cubic polynomial\u00a0x<sup>3<\/sup>\u22123\u221a5x<sup>2<\/sup>+13x\u22123\u221a5, then find all the zeroes of the polynomial.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques28\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 29<\/strong><\/p>\n<p>For which values of\u00a0a\u00a0and\u00a0b, the zeroes of\u00a0q(x)=x<sup>3<\/sup>+2x<sup>2<\/sup>+a\u00a0are also the zeroes of the polynomial\u00a0p(x)=x<sup>5<\/sup>\u2212x<sup>4<\/sup>\u22124x<sup>3<\/sup>+3x<sup>2<\/sup>+3x+b? Which zeores of\u00a0p(x)\u00a0are not the zeroes of\u00a0q(x)?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-polynomials-ques29\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Summary (What we have discussed) Hello! Are you using the NCERT textbook to study Class 10 Maths Chapter 1: &#8220;Real Numbers&#8220;? The Fundamental Theorem of Arithmetic, Euclid&#8217;s Division Lemma, and the distinction between rational and irrational numbers are just a few of the fascinating questions that are covered in this page. During your studies, you [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":7139,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[12,74],"tags":[],"class_list":["post-7104","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Class 10 Maths NCERT Chapter 1 (Real Numbers) Solutions<\/title>\n<meta name=\"description\" content=\"Finding Class 10 Maths NCERT Chapter 1 (Real Numbers) Solutions ? 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