Question

Find '$a$' if $-\frac{1}{2}$ is zero of $g\left(x\right)=8x^3-a{x}^2-a+2$

Answer 1

Given $-\frac{1}{2}$ is zero (root) of the equation

$\Rightarrow g(-\frac{1}{2})=0$

$\Rightarrow 8.\frac{-1}{2^3}-a.\frac{1}{2^2}-a+2=0$

$\Rightarrow \frac{5a}{4}=1$

$\Rightarrow a=\frac{4}{5}$