Can someone explain me what they did in the proof that every extension of degree 2 is normal?

Question

I consider the following proof that every extension of degree $2$ is normal and I got stuck somewhere:

Let $K$ be an extension of $F$ with $[K:F]=2$. Then $K=F(\alpha)$ where $\alpha$ is a root of an irreducible quadratic polonomial $f$ over $F$...

I somehow don't see why $K=F(\alpha)$ can someone explain this to me?

Thanks a lot.