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

Question

1577 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-05T17:27:54

$-2 - sqrt(5)$

Complex zeros and radical zeros always come in conjugate pairs:

$a+-bi " " and a +- sqrt(b)$

The polynomial function is

$f(x) = a(x+1)(x-5)(x+2-sqrt(5))(x+2+sqrt(5))$ ,

where $a$ is a constant.

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