Question

If $x=\frac{1}{2}$ is a zero of the polynomial $f\left(x\right)=8x^3+a{x}^2–4x+2,$
find the value of a.

Answer 1

Given: $f\left(x\right)=8x^3+a{x}^2-4x+2$

$\because x-\frac{1}{2}$ is the root of 𝑓(𝑥).

$\therefore f\left(\frac{1}{2}\right)=0$

$\Rightarrow 8\times (\frac{1}{2}{)}^3+a\times (\frac{1}{2}{)}^2-4\times \frac{1}{2}+2=0$

$\Rightarrow 1+\frac{a}{4}+0=0$

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

$\therefore a=-4$

Hence, the value of 𝑎 is −4.