I am not sure how to answer this can someone please explain it to me:

Question

Find a polynomial with integer coefficients that satisfies the given conditions.

P has a degree 2, and zeros 1+i and 1-i

Thank You!

Answer 1

if R is a root (zero), then x-R is a factor

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

P = x^2 - 2x + 2