Find the degree of $\mathbb Q(\sqrt 2)$ over $\mathbb Q$
We have to find an irreducible polynomial $p(x)$ of $\mathbb Q[x]$ such that $p(\sqrt 2)=0$ and the degree of this polynomial is the degree of $\mathbb Q(\sqrt 2)$ over $\mathbb Q$.
The problem we can find more than one polynomial with these properties, for example $p(x)=x^2-2$ and $q(x)=x^4-4$.
Which polynomial I have to choose and why? Sorry I'm a really beginner, I need help. thanks