Question

What is the simplest polynomial equation that can be written that has roots 4 and 1+2i

Answer 1

p(x) = x^3 -6x^2 +13x -20

Explanation:

We presume you want a polynomial with real coefficients. If so, then there is another complex root, the conjugate of the one given. With three roots, the polynomial will be 3rd degree:

p(x) = (x -4)(x -1+2i)(x -1-2i) = (x -4)((x-1)^2 -(2i)^2) = (x -4)(x^2 -2x +5)

p(x) = x^3 -6x^2 +13x -20