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
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Vieta's Formulas (Wikipedia)
Wikimedia FoundationLead section, first sentenceQuote, Lead section, first sentence
Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
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.
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