Vieta’s Formula about the Sum of Roots of Polynomials

Artur 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 -