Theorem

Bezout's Theorem

Geometry

Bezout's Theorem states that two plane algebraic curves of degrees m and n, with no common component, intersect in exactly m times n points when the points are counted with multiplicity and points at infinity and complex points are included. Named for Etienne Bezout, it is a fundamental result relating the algebraic degree of curves to the geometry of their intersections.

Facts

Statement

In general, the number of common zeros of n polynomials in n indeterminates equals the product of the degrees of the polynomials. 1

Proof Year

1779 1

Classification

Statement Form

Identity or Equation 1

Connections

Source Bezout's Theorem (Wikipedia)

Sources

1. Bezout's Theorem (Wikipedia)

Wikimedia Foundation

lead paragraph, first and second sentences
Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials.
History section
The general theorem was later published in 1779 in Étienne Bézout's Théorie générale des équations algébriques.
Proved By: Étienne Bézout, Lead
It is named after Étienne Bézout.

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Bezout's Theorem

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Proved By