Algebra two question

Question

Find a polynomial equation with real coefficients that has the given roots. 2 and -2i

Answer 1

The complex conjugate of a complex root must also be a root, so you will have 3 roots:

2

-2i

2i

The polynomial is

f(x) = A(x - 2)(x + 2i)(x - 2i) = A(x - 2)(x² + 4)

where A is real and A≠0. You can expand to standard form if you wish.