If $f\in F[t]$ is separable and $E/F$ is an algebraic extension, then how can I be sure that $f$ is separable as an element of $E[t]$?
I thought it is a trivial question...but now I think it is not trivial at all..... How to show that f(t) is separable even as an element of E[t]? Or doesn't it hold??
"Separable" means the roots are distinct in an algebraic closure. The algebraic closure of $E$ is the same field as the algebraic closure of $F$.