Polynomial functions

Question

Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)

−1, 9, 3 − 2i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you have a minimum degree of 4 with zeros

-1

9

3 - 2i

3 + 2i

An example of such a polynomial is

f(x) = (x + 1)(x - 9)[x - (3 - 2i)][x - (3 + 2i)]