Question

How do you make a third degree polynomial with rational coefficients, and it has the roots -4 and 5 + i?

Answer 1

A polynomial with rational coefficients that has a complex root, that root comes in a pair of complex conjugate roots. If you have 5 + i as a root, then you'll have 5 - i as a root, too. You also have -4 as a root. There are your 3 roots.