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

Apr 20, 2017

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