Numerical Solution of Algebraic and Transcendental Equations

Abstract

An algebraic equation of degree n

$$f\left( x \right) \equiv a_0 x^n + a_1 x^{n - 1} + ... + a_n = 0\,\left( {a_0 \ne 0} \right)$$

((1))

with real or complex coefficients a ₀ a _n , has exactly n roots (in general complex) if each root is considered with its appropriate multiplicity (cf. § 1.14).