$x^2 - 2$ [1505A]

The splitting field for $x^{2} - 2 \in \mathbb{Q}[x]$ is $\mathbb{Q}(\sqrt{ 2 })$. $\pm \sqrt{ 2 } \in \mathbb{Q}(\sqrt{ 2 })$. In general, the splitting of $x^{2} + bx + c \in \mathbb{Q}[x]$ is $\mathbb{Q}(\sqrt{ b^{2} - 4c })$.