えーと、英語版だと en.wikipedia.org/wiki/Vieta%27s_formulas HistoryAs reflected in the name, these formulas were discovered by the 16th century French mathematician Francois Viete, for the case of positive roots.
In the opinion of the 18th century British mathematician Charles Hutton, as quoted in (Funkhouser), the general principle (not only for positive real roots) was first understood by the 17th century French mathematician Albert Girard; Hutton writes:
...[Girard was] the first person who understood the general doctrine of the formation of the coefficients of the powers from the sum of the roots and their products. He was the first who discovered the rules for summing the powers of the roots of any equation. （引用おわり）
