The Bring Radical Solution for the Quintic Equation

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Pre-University Paper from the year 2026 in the subject Mathematics - Algebra, grade: 18.5, , language: English, abstract: 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.

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