find the roots of a polynomial

Question

find a polynomial with roots 1, 2, 1+2i, and 1-2i

Answer 1

P(x) = (x-1)(x-2) [ (x-1) + 2i] [ (x-1) - 2i]

= (x^2 - 3x + 2) [ (x-1)^2 + 4]

= (x^2 - 3x + 2) (x^2 -2x + 5)