find a polynomial with real coefficients that has 2, 3+i and 3-2i as zeros

Answer 1

It's a 5th degree polynomial with 5 zeroes, 2, 3+i, 3-2i and the conjugates

(x-2)(x^2-6x+10)(x^2-6x+13) =

x^5 -14x^4 +83x^3 -256x^2 +406x -260