Method for Determining Shared and Repeated Roots in Algebraic Equations

摘要

Common roots shared among all the equations of a set of algebraic equations may be determined by pairing off the equations of the set and repeatedly subtracting, after certain preliminaries. Eventually, all the common roots may be found from an equation of degree equal to the number of common roots, which in many practical cases would be a linear relation or a quadratic. Multiple roots of a single equation, or shared in a set, may be found in a similar manner. The method will also locate approximately the region of almost equal roots of two equations. The process is based on the nature of the roots of a polynomial, which is the algebraic sum of the given polynomials multiplied by constants. (Author)