Answer:
[tex]-\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex]
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 + [tex]\sqrt{3}[/tex], 3 and 4 - 3i, then 2 - [tex]\sqrt{3}[/tex], and 4 + 3i are also roots of the polynomial.
Therefore, since the given polynomial has rational coefficients and some of its roots are , [tex]\sqrt{2}[/tex] and - [tex]\sqrt{13}[/tex], then -[tex]\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex] are also roots of the polynomial.
