Solvability by Radicals
Channel: Andrew Misseldine
Date: 2022-04-13

In this video, we introduce the notion of a field extension by radicals and define what it means for a polynomial to be solvable by radicals. We prove that a polynomial is solvable by radicals only if its Galois group is solvable. Using this, we prove the insolvability of the general quintic equation.

This is lecture 36 (part 2/2) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4230 - Abstract Algebra II at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at: 
https://drive.google.com/file/d/1QgS6I9IHrgFHvul383qKP_ob_RrPiypf/view

This lecture is based upon Sections 23.3 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.