François Viète, Seigneur de la Bigotière was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a privy councilor to both Henry III and Henry IV of France.
Elementary Symmetric Polynomials
A general polynomial of degree n can be written as
with coefficients real or complex numbers and aₙ ≠ 0. By the Fundamental Theorem of Algebra, this polynomial has n (not necessarily distinct) complex roots r₁, r₂, …, rₙ. Vieta’s formulas relate the coefficients aᵢ to signed sums of products of the roots rᵢ as follows: