Related papers: A general formula to solve quintic equation
According to the Abel-Ruffini theorem [1] and Galois theory [2], there is no solution in finite radicals to the general quintic equation. This article takes a different approach and proposes a new method to solve the quintic by iteration of…
This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
The quintic equation with real coefficients $$x^5+5ax^3+5a^2x+b=0$$ is solved in terms of radicals and the results used to sum a hypergeometric series for several arguments.
An irreducible quintic equation is solvable by radicals if and only if its Galois group is solvable. In this work, we provide necessary and sufficient conditions for solvability, expressed in terms of invariants of the quintic.
Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…
In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.
This paper presents new formulary solutions for quantic polynomial equations in general forms, where we present five solutions for any fifth degree polynomial equation with real coefficients, and thereby having the possibility to calculate…
Some physical applications of the Passare-Tsikh solution of a principal quintic equation are discussed. As an example, a quintic equation of state is solved in detail. This approach provides analytical approximations for several problems…
Starting from the solution to Bring's equation the root ambiguity is removed from the solution to the quintic equation. This gives the five complex roots of the quintic equation as indicated by Gauss's Fundamental Theorem of Algebra.r
In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel--Ruffini theorem, which states that the general solution to an algebraic equation of degree five or more cannot be written using…
In this paper, we propose a new method to obtain a solution to a single-parameter Bring quintic equation of the form, $x^{5}+x=a$, where $a$ is real. The method transforms the given quintic equation to an infinite but convergent series…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
It appears that, along with many of my friends and colleagues, I had been brainwashed by the great and tragic lives of Abel and Galois to believe that no general formulas are possible for roots of equations higher than quartic. This seemed…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…
In the late nineteenth century, Felix Klein revived the problem of solving the quintic equation from the moribund state into which Galois had placed it. Klein's approach was a mix of algebra and geometry built on the structure of the…
In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic…
This article provides a simple trigonometric method for determining how many roots of a quintic equation are real and how many are complex, without solving the equation. The approach transforms a depressed quintic $t^5 + mt^3 + nt^2 + pt +…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.