Separability of field extensions

We have seen that for every polynomial f ∈ K[x] over a field K there is a field L ⊇ K over which f splits, say f(x) = c(x − α ₁) ⋯ (x − α_n ) where n = deg f. Now it is possible that the roots α ₁, …, α_n are not pairwise distinct even if f is irreducible.