The second discriminant of a univariate polynomial

• 作者: Dongrning Wang Jing Yang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: Articles
• 页码范围: 1157-1180
• 页数: 24页
• 语种: 英文

摘要

We define the second discriminant D2 of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2rk-ri-rj for all triples of roots ri,rk,rj of f with i ＜ j and j ≠ k,k ≠ i.D2 vanishes if and only if f has at least one root which is equal to the average of two other roots.We show that D2 can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of f.We prove several notable properties and present an application of D2.