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