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The roots of any polynomial equation

Abstract : We provide a method for solving the roots of the general polynomial equation a[n]*x^n+a[n-1]*x^(n-1)+..+a1*x+a0=0. To do so, we express x as a powerseries of s, and calculate the first n-2 coefficients. We turn the polynomial equation into a differential equation that has the roots as solutions. Then we express the powerseries' coefficients in the first n-2 coefficients. Then the variable s is set to a0. A free parameter is added to make the series convergent.
keyword : algebraic equation
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00002529
Contributor : Geert-Jan Uytdewilligen Connect in order to contact the contributor
Submitted on : Friday, August 13, 2004 - 12:13:08 AM
Last modification on : Monday, May 25, 2020 - 5:16:01 PM
Long-term archiving on: : Monday, March 29, 2010 - 9:35:28 PM

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Geert-Jan Uytdewilligen. The roots of any polynomial equation. 2004. ⟨hal-00002529v1⟩

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