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Insert a Root to Extract a Root of Quintic Quickly

2019
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Annales Mathematicae Silesianae
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The usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating odd-powers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a

doi:10.2478/amsil-2018-0013
fatcat:svnwieyturev7efjyfebtbqvr4