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

Formalized Mathematics (2017)

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

top

## Abstract

top
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 ${x}_{1}+{x}_{2}+\cdots +{x}_{n-1}+{x}_{n}=-\frac{{a}_{n-1}}{{a}_{n}}$ , where x1, x2,…, xn are (not necessarily distinct) roots of the polynomial [12]. In the article the sum is denoted by SumRoots.

## How to cite

top

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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.