Hi, I have an examination for Galois theory coming up shortly, and realised there's a question in one of our past papers I don't know how to answer, it reads as follows:
Let be a subfield of and lef be an irreducible polynomial. Prove that has no repeated roots in .
It's worth a fair few marks so I expect the answer's fairly long, but if anyone can provide any ideas how to deal with that I'd be very greatful.
Thanks in advance for your help.