Question

Which of the following is a polynomial with roots -2, -2i, and 2i

Answer 1

x3 - 4x2 + 4x - 16
x3 + 4x2 + 4x + 16
x3 + 2x2 + 4x + 8
x3 - 2x2 + 4x - 8

Answer 2

I would use the factor theorem to check if -2 is a root. But i'm not sure if it works with complex numbers as I have never come across it. You can try though.

The alternative is long winded and not suggested. Divide each one by x+2 and then use quadratic formula to find the complex roots.