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Bézout's theorem
Number of intersection points of algebraic curves and hypersurfaces
Bézout's theorem
In algebraic geometry, 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. It is named after Étienne Bézout. In some elementary texts, Bézout's theorem refers only to the case of two variables, and asserts that, if two plane algebraic curves of degrees d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} have no component in common, they have d 1 d 2 {\displaystyle d_{1}d_{2}} intersection points, counted with their multiplicity, and including points...
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