I have searched for an example of a degree 2 field extension that is not separable.
The example I see is the extension $L/K$ where $L=\mathbb{F}_2(\sqrt t), \ K=\mathbb{F}_2(t) $ where $t$ is not a square in $\mathbb{F}_2.$
Now $\sqrt t$ has minimal polynomial $x^2-t$ over $K$ but people say that $x^2-t=(x-\sqrt t)^2 $. But wouldn't this when expanded be $x^2+t$?
How does this make sense?