Past exam of the options II course of the University of Oxford / 2006 / B / 2 / c / Solution

FactorThe roots are $\pm \sqrt{2},\pm i$, so the splitting field is $\mathbb{Q}(\sqrt{2},i)$. The real quadratic field $\mathbb{Q}(\sqrt{2})$ does not contain $i$, which adds a further degree two. Therefore