Question 1

lf -3 is one of the zeroes of the polynomial $(k-1)x^2+kx+1$, find the value of k.

Solution: 

Given that, one of the zeroes of the quadratic polynomial say $p\left(x\right)=(k-1)x^2+kx+1$ is -3, then $p(-3)=0$
$\Rightarrow (k-1){(-3)}^2+k(-3)+1=0$
$\Rightarrow 9(k-1)-3k+1=0$
$\Rightarrow 9k-9-3k+1=0$
$\Rightarrow 6k-8=0$
$\therefore k=4/3$