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

Jul 20, 2017

#### Answer:

There is not enough information provided to answer this question.

#### Explanation:

Even assuming that we're talking about a polynomial, any numbers might be additional roots of the polynomial.

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.