If 2+sqrt3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.
Another root of the polynomial is 2-sqrt(3).
We know this must also be a root because if 2+sqrt(3) is a root of the polynomial, then the polynomial must be of the form (x - (2+sqrt(3)))(x - (2-sqrt(3))). When you multiply these two factors, you get a polynomial with the roots 2+sqrt(3) and 2-sqrt(3). Therefore, if one root is 2+sqrt(3), the other root must be 2-sqrt(3).