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

1 Answer
Shwetank Mauria
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.

Related questions
See all questions in Complex Conjugate Zeros
Impact of this question
1956 views around the world
You can reuse this answer
Creative Commons License