Vieta's formulas
In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603), more commonly referred to by the Latinised form of his name, "Franciscus Vieta." == Basic formulas == Any general polynomial of degree n P ( x ) = a 0 x n + a 1 x n − 1 + ⋯ + a n − 1 x + a n {\displaystyle P(x)=a_{0}x^{n}+a_{1}x^{n-1}+\cdots +a_{n-1}x+a_{n}} (with the coefficients being real or complex numbers and a0 ≠ 0) has n (not necessarily distinct) complex roots r1, r2, ..., rn by the fundamental theorem of algebra.