Solution
= Solution
The roots are $\pm\sqrt{-5}$, so one root already supplies both. The <polynomial> has no rational root and is irreducible of degree two. Thus its <splitting field> is $\mathbb Q(\sqrt{-5})$, with $\boxed{[K:\mathbb Q]=2}$.
= Solution
The roots are $\pm\sqrt{-5}$, so one root already supplies both. The <polynomial> has no rational root and is irreducible of degree two. Thus its <splitting field> is $\mathbb Q(\sqrt{-5})$, with $\boxed{[K:\mathbb Q]=2}$.