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 …

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.

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 $A$.

Jun 25, 2023 · In this interesting post, it quotes a paper that to write down the complete solution (not in radicals) of the general quintic, one would need "a piece of paper as big as a large asteroid".

Jun 3, 2023 · 3 You are wrong; there are analytic solutions for the general quintic equations. There aren't solutions by radicals, but if you want to learn about solving quintic equations by analytic …

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 …

Jan 28, 2025 · 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 …

Jun 12, 2024 · So you are free to find an extremely special quintic if that makes your job easier, even if it is purely by luck. (2) An explanation for why for every unsolvable quintic with one real root there …