Question

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

Answer 1

`-2 - sqrt(5)`

Explanation:

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.