A degree 4 polynomial with integer coefficients has zeros −1−2i and 1, with 1 a zero of multiplicity 2. If the coefficient of x^4 is 1, then the polynomial is
\(f(x) = (x - 1)^2 (x - (-1-2i))(x - r) \text{ for some } r \in \mathbb C\)
But the polynomial has integer coefficients, so \(r = \overline{-1-2i} = -1+2i\).
\(f(x) = (x^2 - 2x + 1) (x^2 + 2x + 5) \\f(x)= x^4+2x^2-8x+5\)
