Question

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

Answer 1

If (-3+i) is a root, its conjugate, (-3-i) must also be a root. So the factorization has to be something like\[f(x)=a(x-2)(x+3+i)(x+3-i)~~~a \in \mathbb{Q} \]

Answer 2

Your instructor or the author of your book might want you to do the multiplication to get it in simplified form; I'll leave that for you to do.

Answer 3

im clueless ha