关于带参数n次代数方程具有—对纯虚根之充要条件的讨论

ON THE SUFFICIENT AND NECESSARY CONDITIONS OF AN ALGEBRAIC EQUATION WITH PARAMETER OF DEGREE N WHICH HAS A PAIR OF PURE IMAGINARY ZEROS

本文对 n(n≥2)次带参数的代数方程存在一对纯虚根的条件进行了讨论,并以7次方程为例说明了具有一对纯虚根,且剩余根均具负实部之充要条件的论证.

In this paper,we discuss the conditions of an algebraic cguation,with parameter,of degree n (n≥2)which has a pair of pure imaginary zeros.As an example,we give the sufficient and necessary conditions of an equation of degree 7 which has a pair of pure imaginary zeros and the others with negative real parts.