There Is No General Quintic Formula

C. M. Linton

Chapter 7 in Quintic Equations and How to Solve Them, 2025, pp 99-115 from Springer

Abstract: Abstract So far, we have given a fairly detailed account of the roots of polynomials, described the basic building blocks of Galois theory and shown how these ideas apply to quadratics, cubics and quartics. For quadratics, there is a simple formula which involves taking a single square root and once we admit complex numbers into our lexicon this always yields two solutions, one for each of the possible square roots.

Date: 2025
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DOI: 10.1007/978-3-032-01658-4_7

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