High Quality Content by WIKIPEDIA articles! In mathematics, a polynomial is a function of the form p(x) = a_0 + a_1 x + cdots + a_n x^n, quad xin mathbb{C} where the coefficients a_0, ldots, a_n are complex numbers and a_nneq 0. The fundamental theorem of algebra states that polynomial p has n roots. The aim of this page is to list various properties of these roots.The n roots of a polynomial of degree n depend continuously on the coefficients. This means that there are n continuous functions r_1,ldots, r_n depending on the coefficients that parametrize the roots with correct multiplicity.This result implies that the eigenvalues of a matrix depend continuously on the matrix. A proof can be found in Tyrtyshnikov(1997).The problem of approximating the roots given the coefficients is ill-conditioned. See, for example, Wilkinson's polynomial.

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