Vieta's Formulas relate the coefficients of a polynomial to sums and products of its roots, expressing each elementary symmetric function of the roots, such as their sum or their product, as a ratio of the polynomial's coefficients up to a sign determined by the degree of that function. Named for Francois Viete, they let a polynomial's coefficients be read directly from properties of its roots and are used throughout algebra without needing to solve for the roots themselves.
Facts
StatementVieta's formulas relate the coefficients of a polynomial to sums and products of its roots. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Wolfram MathWorld: Vieta's Formulas
Proved By
Source Wolfram MathWorld: Vieta's Formulas
Sources
1. Vieta's Formulas (Wikipedia)
Wikimedia FoundationLead section, first sentence
Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
In Group: Polynomials and Elementary Algebra, Lead section
mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named
View the Source 2. Francois Viete (1540 - 1603), Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsBiography narrative, algebraic notation paragraphQuote, Biography narrative, algebraic notation paragraph
Viete introduced the first systematic algebraic notation in his book In artem analyticam isagoge published at Tours in 1591.
Wolfram MathWorld: Vieta's Formulas
Wolfram MathWorldIn Branch: Algebra, Subject classifications
Algebra Polynomials
Proved By: François Viète, Lead
The theorem was proved by Viète (also known as Vieta, 1579) for positive roots only, and the general theorem was proved by Girard.
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