Determine the Galois group of $X^4 - 2X^2 +2$ over $\Bbb Q$ and prove $\sqrt 2 \in \Bbb Q(\alpha)$ where $\alpha$ is a root of $X^4 - 2X^2 +2$
Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $