0
$\begingroup$

Let $E/F$ be an extension and $f \in F[X]$. I was reading a statement saying if $f$ is separable and has multiple roots (repeated roots), these roots must be in $F$. I don't understand this. Isn't the fact that $f$ is separable supposed to mean that it has distinct roots? And why would they be in $F$?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.