# How do you find all additional roots given the roots 5-sqrt6 and -2+sqrt10?

Jul 20, 2017

If we require rational coefficients, the the conjugates $5 + \sqrt{6}$ and $- 2 - \sqrt{10}$ are also roots.
But for all we know $7$ might also be a root. and $9 - \sqrt{7} i$ might be a root and so on.