If $\sqrt 2 - i$ is a root of $x^5-x^4-2x^3+mx^2+9x+m-11=0$, $m \in \Bbb Q$ find m and the other roots. My question is what other roots can i deduce from what is given? Is $\sqrt 2 + i$ the only one i can deduce or are $-\sqrt 2 - i$ and $-\sqrt 2 + i$ also "valid" (by valid i mean deducible without knowing the answer).
More generally if i have natural coefficient polynomial with a given a root like $\sqrt a + bi$ can i say that $\sqrt a - bi$, $-\sqrt a + bi$ and $-\sqrt a - bi$ are also roots?