##  [Resultant](/resultant) 

  ##  [Resultant](https://algebra.quantumdictionary.io/resultant-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A scalar, often given as the determinant of a suitably constructed matrix (for two univariate polynomials the Sylvester matrix), that vanishes exactly when the input polynomials have a nontrivial common root in projective space. The resultant is an elimination object: it compresses the condition “exists x such that f(x)=g(x)=0” into a single polynomial expression in the coefficients.