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 more appropriate.

Feb 2, 2016 · $ (1)$ From Galois theory it is known there is no formula to solve a general quintic equation. But it is known a general quintic can be solved for the 5 roots exactly. Back in 1858 …

Jul 2, 2016 · 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 …

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.

Nov 16, 2022 · In short, I am looking for a precise example for the solvable quintic whose roots are the most complicated. Of course, the example this type of quintic itself can be interesting.

Possible Duplicate: Why is it so hard to find the roots of polynomial equations? For polynomials (with real coefficients), in degrees 2, 3, 4, there are the quadratic, cubic, and quartic formula,

Jan 25, 2013 · A recent question asks what makes degree 5 special when considering the roots of polynomials with integer coefficients etc. One answer is that the Galois Group of $S ...

Aug 10, 2020 · I was on Wolfram Alpha exploring quintic equations that were unsolvable using radicals. Specifically, I was looking at quintics of the form $x^5-x+A=0$ for nonzero integers $A$.

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 quintics (and note …

Jul 12, 2023 · I. Principal quintic First reduce the quintic to principal form, and yours is special in that its Tschirnhausen transformation needs only rational coefficients.