How do you write a polynomial function with the given zeros. 3-2i

Question

I need to know how to solve this question.

How do you write a polynomial function of least degree with integral coefficients that has the given zeros.

 

Problem: 3-2i

 

Thank you!

Answer 1

If 3-2i is a zero of a polynomial with integer coefficients, then the conjugate 3+2i must also be a zero of this polynomial. Therefore, the polynomial is at least quadratic (degree 2):

 

(x - (3-2i))(x - (3+2i)) = x² -6x + 13

Answer 2

Cynthia, are you sure there's not more to this question?  What degree is the polynomial supposed to be?