Question

A cubic polynomial with rational coefficients has the roots 6 + *sqrt* 6 and 2/3 . Find one additional root.

Answer 1

The correct answer is 6 - sqrt(6)

We know this because when we solve with the quadratic equation, the numbers come out with a constant plus and minus the discriminant under a square root symbol. You can see that below in the quadratic equation. 

$\frac{-b +/- \sqrt{ b^{2} - 4ac } }{2a}$

So seeing that one answer is 6 + sqrt(6), we can assume 6 is the discriminat and 6 is the constant. Thus giving us the new answer as well.