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

##### 1 Answer

Sep 18, 2016

The additional zeros are

#### Explanation:

Complex zeros always occur in pairs in the form of complex conjugates

The complex conjugate of

Similarly, zeros containing square roots must also come in pairs. If the polynomial has a zero of

Think about the quadratic formula

If the discriminant

If the discriminant is positive but not a perfect square, there will also be two zeros of the form