Vieta’s Formula about the Sum of Roots of Polynomials

Abstract

SummaryIn the article we formalized in the Mizar system [2] the Vieta formula about the sum of roots of a polynomial anxn + an−1xn−1 + ··· + a1x + a0 defined over an algebraically closed field. The formula says that x1+x2+⋯+xn−1+xn=−an−1an , where x1, x2,…, xn are (not necessarily distinct) roots of the polynomial [12]. In the article the sum is denoted by SumRoots.