In the cubic equation

the constants p and q are real and

is a root. I want to find the other two roots but I'm a little lost at what to do to get one of them.

I know that

is a root as the conjugate is always a root, and I also know that a cubic equation has either one or three real roots - so it follows that the other root I need to find is real.

I tried finding the sum and product of the roots but I can't because I don't know what p and q are yet - I tried using an algebraic division method but the same can be said for this, and I don't know any other method to get the other root.

The second part of the question asks to find the values of p and q, but I take it that there's a way to get the other root without getting these first? Could anyone suggest a method?

Thanks if you can help me out