# If a polynomial function with rational coefficients has the zeros -1, 5, -2+sqrt5, what are the additional zeros?

May 5, 2017

$- 2 - \sqrt{5}$

#### Explanation:

Complex zeros and radical zeros always come in conjugate pairs:

$a \pm b i \text{ } \mathmr{and} a \pm \sqrt{b}$

The polynomial function is

$f \left(x\right) = a \left(x + 1\right) \left(x - 5\right) \left(x + 2 - \sqrt{5}\right) \left(x + 2 + \sqrt{5}\right)$,

where $a$ is a constant.