Question

Find the polynomial p(x) with roots 1+i and 1-i

Answer 1

Required root is p(x) = (x - (1 + i))(x - (1 - i)) = (x - 1 - i)(x - 1 + i) = x^2 - x + ix - x + 1 - i - ix + i + 1 = x^2 - 2x + 2

P(x) = x^2 - 2x + 2