【摘 要】
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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 wh
【机 构】
：
BDBC,LMIB and School of Mathematics and Systems Science,Beihang University,Beijing 100191,China;SMS,
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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.
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