Mathematica Eterna
Open Access

Abstract

Solving Polynomial Equations

Mircea Ion Cˆırnu

In this paper are given simple methods for calculating approximate values of the extreme roots of polynomials - roots dominant and dominated in modulus. They are obtained by improving old methods, namely the Newton’s radical method and the Daniel Bernoulli’s ratio method. The eigenvalues of a square matrix can be also calculated, even if it is not known its characteristic polynomial. Unlike the old methods, the present methods can calculate multiple and complex roots. By suitable variable changes, can be solved polynomials which initially have not extreme roots. In this way can be calculated complex roots of the polynomials with real coefficients and radicals of real or complex numbers. Using the results from a previous Author’s work, finally shown how the present methods can be used to solve the nonlinear algebraic equations. Throughout the paper are given illustrative examples.