1. Prove that if F is an extension field of K of degree 2, then F is the splitting field over K for some polynomial.
I found a corollary in my book saying if F is a finite extension of K, and u in F then the degree of u over K is a divisor of [F:K]. I have a feeling that may help.
We have a splitting field if [F:K]<=n! with n being the degree.
So we want to show we have [F:K]<=2 since 2 was the degree.