The Bring Radical Solution for the Quintic Equation

Thèse Scolaire , 2026 , 5 Pages , Note: 18.5

Mathématiques - Algèbre

This paper studies a quintic equation that can be reduced to Bring–Jerrard form and solved using the Bring radical. We consider the reduced trinomial quintic

x^5 + p x + q = 0

and express its solution in terms of the Bring radical, defined as the principal root of

t^5 + t + u = 0.

The result provides an exact implicit representation of the root in the complex domain, subject to principal branch choices for fractional powers. The special case p = 0 reduces to the simple fifth-root solution

x = fifth root of (−q).

The method is exact for reduced quintic equations and illustrates the role of the Bring radical in algebraic solution theory.

• Note: 18.5
• Auteur: Fazal Rehman (Auteur)
• Année de publication: 2026
• Pages: 5
• N° de catalogue: V1714624
• ISBN (PDF): 9783389186787
• Langue: anglais
• mots-clé: bring, radical, solution, quintic, equation