First the easy one (I think):(adsbygoogle = window.adsbygoogle || []).push({});

Show that x^{4}-22x^{3}+1 is irreducable (is that how it's spelled?) over Q.

Now the one that's giving me a headache:

Suppose E/F, when [E:F]=2, and char(E)>2. Prove that there exists u in E, s.t. E=F(u), when u is a root of p(x)=x^2-a, for a in F.

Tried all kinds of stuff, it just won't lead me anywhere. I guess it's probably easy, but it's bothering me.

Thanks in advance!

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# Fields- a couple of questions

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