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(-\frac12\right) = 8\left(-\frac12\right)^3 - a\left(-\frac12\right)^2 - \left(-\frac12\right) + 2 = 0`

`-1 - \frac a4 + \frac12 + 2 = 0`

`-\frac a4 = -\frac32`

`\boxed{a = 6}`