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In mathematics, a univariate polynomial is an expression of the form : where the belong to some field, which, in this article, is always the field of the complex numbers. The natural number is known as the degree of the polynomial. In the following, will be used to represent the polynomial, so we have : A root of the polynomial is a solution of the equation : that is, a complex number such that . The fundamental theorem of algebra combined with the factor theorem states that the polynomial ''p'' has ''n'' roots in the complex plane, if they are counted with their multiplicities. This article concerns various properties of the roots of , including their location in the complex plane. ==Continuous dependence on coefficients== The ''n'' roots of a polynomial of degree ''n'' depend continuously on the coefficients. This result implies that the eigenvalues of a matrix depend continuously on the matrix. A proof can be found in a book of Tyrtyshnikov.〔 The problem of approximating the roots given the coefficients is ill-conditioned. See, for example, Wilkinson's polynomial. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「properties of polynomial roots」の詳細全文を読む スポンサード リンク
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