Degree 3; zeros: -5, 5 - 5i

Question

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Answer 1

The remaining zero is 5 + 5i.

The remaining zero must be the complex conjugate of the only given complex zero.

This is to ensure that the resulting polynomial

(x + 5)(x - 5 + 5i)(x - 5 - 5i)

has all real coefficients.