Corpus ID: 118897445

The roots of any polynomial equation

  title={The roots of any polynomial equation},
  author={Geert-Jan Uytdewilligen},
  journal={arXiv: Classical Analysis and ODEs},
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. 


Advanced Engineering Mathematics.
PART A: ORDINARY DIFFERENTIAL EQUATIONS (ODE'S). Chapter 1. First-Order ODE's. Chapter 2. Second Order Linear ODE's. Chapter 3. Higher Order Linear ODE's. Chapter 4. Systems of ODE's Phase Plane,Expand
On the theory of the Transcendental Solution of Algebraic Equations
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