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.
- Quote paper
- Fazal Rehman (Author), 2026, The Bring Radical Solution for the Quintic Equation, Munich, GRIN Verlag, https://www.grin.com/document/1714624
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