Question

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

Answer 1

Answer:

$-\sqrt{2}$ and $\sqrt{13}$

Step-by-step 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 + $\sqrt{3}$, 3 and 4 - 3i, then 2 - $\sqrt{3}$, and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are , $\sqrt{2}$ and  - $\sqrt{13}$, then -$\sqrt{2}$ and $\sqrt{13}$ are also roots of the polynomial.