Question

if x is equal to minus 1 upon 2 is a zero of the polynomial PX is equal to 8 x cube minus a x square - 8 x + 2 find the value of a​

Answer 1

$8 {x}^{3} - a {x}^{2} - 8x + 2 \\ x = - \frac {1}{2} \\ substitute \: - \frac{1}{2} \: in \: equation \\ 8 { ( - \frac{ 1}{2} )}^{3} - a {( - \frac{1}{2} )}^{2} - 8 \times - \frac{1}{2} + 2 \\ 8 \times - \frac{1}{8} + \frac{a}{4} + 4 + 2 \\ - 1 + \frac{a}{4} + 6 = 0 \\ \frac{a}{4} + 5 = 0 \\ \frac{a}{4} = - 5 \\ a = - 20$