In characteristic zero or over a finite field, every algebraic extension is separable.Suggest a slogan
Let \(k\) be a field with \(\ch k=0\) or \(k\) finite. Then every algebraic extension \(L/k\) is separable.
Such a field is perfect. For \(\alpha\in L\), the minimal polynomial of \(\alpha\) over \(k\) is irreducible in \(k[x]\), hence separable, so \(\alpha\) is separable over \(k\).