I think after quintic it becomes cumbersome to name them (since the prefixes become increasingly more complex). Thus, I feel like "degree seven" or "seventh degree" polynomial is …

Feb 2, 2016 · Galois Theory tells us that the roots of a general quintic can not be obtained by the use of radicals alone (that is, with the usual operations of arithmetic and taking n n -th roots for …

2 I am trying to get my head around Galois theory and the unsolvability of the general quintic (or equations of higher degree). The fundamental theorem of algebra states that a polynomial …

Quintic polynomial with Galois Group A5 A 5 Ask Question Asked 12 years, 5 months ago Modified 12 years, 5 months ago

The insolvability of the quintic is about quintic equations in general, not about particular quintics such as this one. It says that there does not exist an analogue of the quadratic formula for …

Sep 7, 2019 · Arnold's proof for the insolvability of the quintic Ask Question Asked 5 years, 9 months ago Modified 5 years, 8 months ago

Jul 30, 2014 · I have been pondering over this question for a few months now. Why exactly do quintic equations have no closed general expression for their roots? Looking at graphs and …

I know that quintics in general are unsolvable, whereas lower-degree equations are solvable and the formal explanation is very hard. I would like to have an intuitive reasoning of why it is so,

Mar 18, 2015 · According to a paper by Dummit, "SOLVING SOLVABLE QUINTICS", a quintic is solvable by radicals iff its Galois group is is contained in the Frobenius group F20 F 20 of …

Jun 12, 2016 · If no, the quintic can be solved by radicals because polynomials with degree less than 5 can always be solved by radicals. If yes, you have to find out the galois-group.