Let K be a field, and let P be separable and irreducible over K. Let L be a splitting field of P over K.
I want to show that the fields K(u) and K(v) are isomorphic, where u and v are roots of P, and then extend this isomorphism.
I have shown that they are isomorphic, but to extend I need to show that K(u) and K(v) are algebraically closed - I was wondering could someone explain why this is the case?