# Viète theorem

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on roots

A theorem which establishes relations between the roots and the coefficients of a polynomial. Let be a polynomial of degree with coefficients from some field and with leading coefficient 1. The polynomial splits over a field containing all the roots of (e.g. over the splitting field of , cf. Splitting field of a polynomial) into linear factors:  where are the roots of , . Viète's theorem asserts that the following relations (Viète's formulas) hold:      F. Viète  proved this relation for all , but for positive roots only; the general form of Viète's theorem was established by A. Girard .

How to Cite This Entry:
Viète theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Vi%C3%A8te_theorem&oldid=14535
This article was adapted from an original article by V.N. Remeslennikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article