Annales Mathematicae Silesianae (Sep 2019)

Insert a Root to Extract a Root of Quintic Quickly

  • Kulkarni Raghavendra G.

DOI
https://doi.org/10.2478/amsil-2018-0013
Journal volume & issue
Vol. 33, no. 1
pp. 153 – 158

Abstract

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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 cubic equation; thus one needs to solve the cubic equation.

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