Question

A polynomial function P(x) with rational coefficients has the roots sqrt 2 and - sqrt 13. Find two additional roots.

Answer 1

`-√(2)` and
`√(13)`

Explanation:

Given a polynomial with rational coefficients, its irrational and complex roots would occur in conjugate pairs.

For example, if the roots of a polynomial are 2 +
`√(3)`, 3 and 4 - 3i, then 2 -
`√(3)`, and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are ,
`√(2)` and -
`√(13)`, then -
`√(2)` and
`√(13)` are also roots of the polynomial.