Question

A Cubic Polynomial with rational coefficients has the roots 6 + SQRT6 and 2/3 FInd one additional root.

Answer 1

Answer:  6 - sqrt(6)

This is because of the rule that if we have rational coefficients, then one root of $a+\sqrt{b}$ must have a conjugate pair of $a-\sqrt{b}$. Multiplying the conjugates will have the square roots cancel out.

For more information, check out the difference of squares rule.