## You are here

Homeproof of Vieta's formula

## Primary tabs

# proof of Vieta’s formula

Proof: We can write $P(x)$ as

$P(x)=a_{n}(x-r_{1})(x-r_{2})\ldots(x-r_{n})=a_{n}(x^{n}-S_{1}x^{{n-1}}+S_{2}x^% {{n-2}}-\ldots+(-1)^{n}S_{n}).$ |

Since we also have that

$P(x)=a_{n}x^{n}+a_{{n-1}}x^{{n-1}}+\ldots a_{{1}}x+a_{{0}},$ |

setting the coefficients equal yields

$a_{n}(-1)^{{i}}S_{i}=a_{{n-i}}$ |

which is what the theorem stated.

Major Section:

Reference

Type of Math Object:

Proof

Parent:

## Mathematics Subject Classification

12Y05*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff