The roots of any polynomial equation
Uytdewilligen, Geert-Jan
HAL, hal-00002529 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-08-20
Classification:  algebraic equation,  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 
@article{hal-00002529,
     author = {Uytdewilligen, Geert-Jan},
     title = {The roots of any polynomial equation},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00002529}
}

Uytdewilligen, Geert-Jan. The roots of any polynomial equation. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002529/