# Vieta’s Formula about the Sum of Roots of Polynomials

Formalized Mathematics (2017)

- Volume: 25, Issue: 2, page 87-92
- ISSN: 1426-2630

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topArtur Korniłowicz, and Karol Pąk. "Vieta’s Formula about the Sum of Roots of Polynomials." Formalized Mathematics 25.2 (2017): 87-92. <http://eudml.org/doc/288310>.

@article{ArturKorniłowicz2017,

abstract = {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.},

author = {Artur Korniłowicz, Karol Pąk},

journal = {Formalized Mathematics},

keywords = {roots of polynomials; Vieta’s formula},

language = {eng},

number = {2},

pages = {87-92},

title = {Vieta’s Formula about the Sum of Roots of Polynomials},

url = {http://eudml.org/doc/288310},

volume = {25},

year = {2017},

}

TY - JOUR

AU - Artur Korniłowicz

AU - Karol Pąk

TI - Vieta’s Formula about the Sum of Roots of Polynomials

JO - Formalized Mathematics

PY - 2017

VL - 25

IS - 2

SP - 87

EP - 92

AB - 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.

LA - eng

KW - roots of polynomials; Vieta’s formula

UR - http://eudml.org/doc/288310

ER -

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