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Vieta’s Formula about the Sum of Roots of Polynomials

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Korniłowicz A., Pąk K.

Formalized Mathematics

2017

tom 25

nr 2

87-92

In 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 $x_1 + x_2 + \cdots + x_{n - 1} + x_n = - {{a_{n - 1} } \over {a_n }}$ , where x1, x2,…, xn are (not necessarily distinct) roots of the polynomial [12]. In the article the sum is denoted by SumRoots.

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1 Formalized Mathematics

1 Korniłowicz A.

1 Pąk K.

1 2017

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Vieta’s Formula about the Sum of Roots of Polynomials