Question

If x=-1/2 is a zero of the polynomial p(x)=8x^3-ax^2-x+2, find the value of a.

Answer 1

If $x=-\frac12$ is a zero, then $p\left(-\frac12\right) = 0$. Solve this equation for $a$.

$p\left(-\dfrac12\right) = 8\left(-\dfrac12\right)^3 - a\left(-\dfrac12\right)^2 - \left(-\dfrac12\right) + 2 = 0$

$-1 - \dfrac a4 + \dfrac12 + 2 = 0$

$-\dfrac a4 = -\dfrac32$

$\boxed{a = 6}$