Question

A polynomial function of degree 4 with real coefficients could have -3, 2 + i, 2 - i, and -3 + 5i as its zeros? is that right?

Answer 1

All complex roots come in conjugate pairs. So 2+i is coupled with 2-i while -3+5i is paired with -3-5i

That's 4 roots so far, but we also have the root of -3. We now have 5 roots total. So it's a 5th degree polynomial or larger.

Answer 2

complex roots in polynomials with only real coefficients, to be picky...