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 · Back in 1858 Hermite and Kronecker independently showed the quintic can be exactly solved for (using elliptic modular function). Also I think they're maybe other solution for the quintic …

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 ...

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.

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 …

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,

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 $A$.

May 28, 2023 · The Galois-theoretic proof of the unsolvability of the quintic is, more precisely, a proof that there are quintic (and higher) polynomials over $\Bbb Q$ whose splitting field extension cannot …

Jul 18, 2024 · A generic quintic threefold has 2875 lines. Is there an example of a quintic threefold explicitly defined by a polynomial that can be proven to have exactly 2875 distinct lines?