Abstract: Through some-years teaching experience，a used for solving breakaway points in root-locus is presented in this article.This method is helpful for students to understand the nature of root-locus.Otherwise，a contrastive analysis between the tentative dichotomy and the classical Newton remainder axiom both from theoretical and emulational results is worked out.The result of analysis shows that the tentative dichotomy has the merits of more operation speed and more easily controllable precision.

Key words: root-locus, breakaway point, numerical methods, dichotomy

摘要： 在多年教学经验基础上总结出一种求解根轨迹分离点的二分试探数值解法，经验证明此法有助于对根轨迹本质含义的理解，同时将此法从理论和仿真结果上与经典的牛顿迭代法进行了对比研究，结果表明二分迭代法具有运算速度快、易于精度控制等优点。

关键词: 根轨迹, 分离点, 数值解法, 二分迭代法