Vieta’s Formula about the Sum of Roots of Polynomials

In the article we formalized in the Mizar system [2] the Vieta formula about the sum of roots of a polynomial a_nxⁿ + a_n−1xⁿ⁻¹ + ··· + a₁x + a₀ defined over an algebraically closed field. The formula says that x1+x2+⋯+xn−1+xn=−an−1an$x_1 + x_2 + \cdots + x_{n - 1} + x_n = - {{a_{n - 1} } \over {a_n }}$ , where x₁, x₂,…, x_n are (not necessarily distinct) roots of the polynomial [12]. In the article the sum is denoted by SumRoots.