Question

find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3+i

Answer 1

If you have roots a1, a2, ..., an you can express the polynomial as (x-a1)(x-a2)...(x-an)

Answer 2

Note that for an equation with real coefficients, complex roots always come in conjugate pairs. If a+bi is a root, a-bi will also be a root.