Question

Find a cubic equation with integral coefficients and roots -1/3 and 2+2i.
I know I need to use sum and product of the roots, but that's about it.

Answer 1

All imaginary roots come in conjugate pairs, so your unwritten root is 2-2i.

Set x to each root and then produce a factor

x=2+2i so x-2-2i=0 and (x-2-2i) is one factor.

Multiply your three factors out and you'll have the cubic polynomial you seek.

Answer 2

So:
(2+2i-x)(x+1/3)(2-2i-x)=0

Answer 3

But do you know how to do this by using the sum and product?

Answer 4

No, I don't.

Answer 5

Okay, thanks anyways.