Question

If 2+sqrt(3) is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.

Answer 1

Hey :)

Irrational roots will always come in conjugate pairs.
So if 2+sqrt(3) is a root, then 2-sqrt(3) is also a root.

This also applies to complex roots.
If a+bi is a root, then a-bi is also a root of the polynomial.

Answer 2

The irrational conjugate roots theorem says:
Let p(x) be any polynomial with rational coefficients. If
a + b*sqrt(c) is a root of p(x), where sqrt(c) is irrational and
a and b are rational, then another root is a - b*sqrt(c).

http://mathforum.org/library/drmath/view/52607.html