Suppose the polynomial f(x) has the following roots: 1+6sqrt2, 2−sqrt6, and 6+sqrt2. If f(x) has only rational coefficients, the Irrational Root Theorem indicates that f(x) has at least three more roots.

Question

What are the three additional roots that f(x) must have?

Answer 1

If you have x + y sqrt 2 you better have x- y sqrt 2
because you need sqrt 2 * sqrt 2 to get those original rational coefficients

Answer 2

thank you so much Damon