The roots of any polynomial equation

Geert-Jan Uytdewilligen (1)

1 FONTYS - Fontys Hogeschool Toegepaste Natuurwetenschappen = Fontys University of Applied Sciences

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.

Mots clés: algebraic equation

Domaines: Analyse classique [math.CA]

Geert-Jan Uytdewilligen. The roots of any polynomial equation. 2004. ⟨hal-00002529v2⟩