一类代数方程的摄动解

The perturbed solutions to a class of algebraic equation

设f(x),g(x)分别为复数域上的 m和 n次多项式  利用直接展开法分 m≥n和 m<n两类情况讨论 了形如 f(x)＋ ε g(x)=0的摄动代数方程[1]的近似解， 得到了其根的两项展开式的3个公式由前2个公式根据退化方程[2]的单根或重根可给出该方程的m个根由第3个公式可给出关于m<n情形其余n－ m个根， 并推广了文[1]相应的结果

Let f(x) and g(x) be two polynomials in complex number field with their orders being m and n respectively. By using direct expanding method, the approximate solutions of the perturbed algebraic equation such as f(x)＋ ε g(x)=0 for m≥ n and m<n, and three formulas about two terms expansion of its roots are obtained. The m roots can be given according to the single root or pluri－ root of its degenerate equation from the first two. The rest n－ m roots for m<n can be given according to the third, and the relative result of [1] is generalized.