On the Laguerre method for separating the roots of algebraic equations

Abstract

where f--f(x), f(x) = 0 is an algebraic equation of degree N with real roots and x an arbitrary real number, separate the roots of the equation. This proposition was also discussed by Ch. Hermite [2 ] and by E. Bodewig [N]. According to the proposition there will be at least one root of the equation between u and v. A generalization of the relation (1), given in the following section gives a method for separating just one root and, in fact, to evaluate it.