Question

If $b$ is zero of the polynomial $p\left(x\right)=a{x}^2-3(a-1)x-1$ , then find the value of $a$.

Answer 1

We have,

$p\left(x\right)=a{x}^2-3(a-1)x-1$

Since $b$ is the zero of the given polynomial.

Therefore,

$a{b}^2-3(a-1)b-1=0$

$a{b}^2-3ab+3b-1=0$

$a(b^2-3b)+3b-1=0$

$a(b^2-3b)=-(3b-1)$

$a=\frac{-(3b-1)}{b^2-3b}$

$a=\frac{1-3b}{b^2-3b}$