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

Answer:

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.