Question

Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1

Answer 1

if 1+i is a root, so is 1-i. So, the factors are

(x+1)(x-(1+i))(x-(1-i))
(x+1)((x-1)^2 - i^2)
(x+1)(x^2-2x+2)
x^3-x^2+2