Question

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

Answer 1

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+sqrt6` and `-2-sqrt10` are also roots.

But for all we know `7` might also be a root. and `9-sqrt7i` might be a root and so on.