(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to come up with an example of a quartic polynomial over a field F which has a root in F, but whose splitting field isn't the same as its resolvent cubic.

2. Relevant equations

3. The attempt at a solution

Well, I know the splitting field of the cubic resolvent is contained in the splitting field of the quartic, so that narrows down the choices quite a bit. But frankly I'm not even sure this is possible because the cubic resolvent is pretty much defined in terms of the roots of the quartic.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Example in Abstract Algebra

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**