International Journal of Pure and Applied Mathematics Research
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Volume 2, Issue 2, October 2022 | |
Research PaperOpenAccess | |
Approximate Solution of Quintic and Higher-Degree Equations |
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Jorge A. Franco1* |
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1Independent researcher, ORCID: 0000-0001-5951-1129. E-mail: georgeafr@gmail.com
*Corresponding Author | |
Int.J.Pure&App.Math.Res. 2(2) (2022) 10-23, DOI: https://doi.org/10.51483/IJPAMR.2.2.2022.10-23 | |
Received: 03/06/2022|Accepted: 19/10/2022|Published: 05/10/2022 |
The general exact solution by radicals of the De Moivre equations of any degree is presented. But, since it is impossible to obtain the general exact solution of any quintic by radicals, except those of De Moivre or binomial, approximate method for solving any monic quintic, sextic, ... or 30th degree equation is proposed, namely, by decomposing them into two factors of degrees n–1 and 1, we obtain n unknown coefficients and n equations, which allow us to know all their roots, with a high degree of approximation.
Keywords: Exact solution of De Moivre’s equation by radicals of 3rd, 4th or any degree, Solution of any monic Quintic, Sextic, Septic, … , or 30th degree equation by a general approximate method
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