Question

If x = - $\frac{1}{2}$ is a zero of the polynomial p(x)

= $8x^3-a{x}^2$ - x + 2, find the value of a.

Answer 1

p(x) = $8x^3-a{x}^2$ - x + 2

$\because x=-\frac{1}{2}$ is its zero, then

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

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

$\Rightarrow -1-\frac{a}{4}+\frac{1}{2}+2=0$

$\Rightarrow \frac{3}{2}-\frac{a}{4}=0\Rightarrow \frac{a}{4}=\frac{3}{2}$

$\Rightarrow a=\frac{3\times 4}{2}=6$

$\therefore$ a = 6