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

1 Answer
Apr 20, 2017

At least 2+2i

Explanation:

A polynomial function with rational coefficients always has pair of complex conjugate numbers as it's zeros.

As the polynomial has the zeros 2-2i, 1-2i, 1+2i, of which last two are pair of complex conjugate numbers, but first zero i.e. 2-2i does not have its conjugate 2+2i as zero. Hence, the polynomial must have atleast 2+2i as additional zero.

There could be more additional zeros, but they would have to be either rational numbers or pair of complex conjugate numbers.