Types of polynomial functions. Quadratic, cubic, quartic, quintic,
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 …
polynomials - Discriminant of Quintic (Galois theory)?
2016年4月10日 · Just for reference: the discriminant of your polynomial is $$3125 p^4-256 N^5 p^5.$$ I computed it using Mathematica.
abstract algebra - Quintic polynomial with Galois Group $A_5 ...
$\begingroup$ @YACP has put the guts of a solution below, except for computing the discriminant - on a good day I can remember the formula for the discriminant of a cubic, but a …
Is there a formula for the roots of a Quintic Equation?
2016年2月2日 · $(1)$ 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 …
polynomials - Solving quintic equations of the form $x^5-x+A=0 ...
2020年8月10日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Solving a Quintic polynomial - Mathematics Stack Exchange
quintic solution to noncommutative polynomial. 1. Representing a Quintic Polynomial as the Product of its ...
Intuitive reasoning why are quintics unsolvable
Let the roots of an equation be A, B, C, etc. We are told that the unsolvability of the general quintic equation is related to the unsolvability of the associated Galois group, the symmetric …
Why can't there be a quintic formula? [duplicate]
$\begingroup$ It is possible to express the roots of a quintic polynomial with real coefficients in terms of the coefficients, using just the operations of addition, subtraction, multiplication, …
Applying trigonometry in solving quintic polynomials?
2015年12月26日 · So I came across the unsolvable quintic polynomial noticing that solutions can be found by connections with ellipses and such here. But more importantly, I was considering …
What does insolvability of the quintic mean exactly?
Suppose I had the quintic equation $(x+1)(x+2)(x+3)(x+4)(x+5)=0$. Does the insolvability theory mean that I can only get approximations because the root is in general an irrational number, or …