对方程有根问题的探讨  

Discussion on the problem of equation with roots

作　　者：孙艳君[1] SUN Yanjun(School of Mathematics,College of Boda Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学博达学院数学学院,吉林四平136000

出　　处：《渤海大学学报（自然科学版）》2023年第3期250-253,共4页Journal of Bohai University:Natural Science Edition

基　　金：吉林省成人教育协会十四五成人(继续)教育科研规化项目(No:2022CJY026).

摘　　要：方程有根问题是高等数学中的常见问题,在很多证明或讨论题中经常出现,也是历年考研中的常见题型.这类问题种类繁多,而且难度比较大,但是在教材中涉及到的内容却非常有限,相关文献涉及此类问题较少,而且方法单一,学生很难把握.因此,如何选择正确的方法是解决这类问题的关键.在解题过程中,根据问题的条件和结论的特点,通过逆向分析、综合运用数学基本原理,选择正确的方法,可以使有些复杂的问题迎刃而解.因此将分析这类问题的特点,总结规律,并给出几类常见的题型和常用的解题方法,为此类问题提供一定的理论依据.The problem of equation howing roots is a common problem in advanced mathematics,which often appears in many proof or discussion questions.It is also a common type of question in the postgraduate entrance examination.There are many types of such problems,and the difficulty is relatively large.However,the content involved in the textbook is very limited,and the relevant literature deals with such problems,and the method is single,which is difficult for students to grasp.Therefore,how to choose the right method is the key to solving this kind of problem.In the process of solving the problem,according to the conditions of the problem and the characteristics of the conclusion,by reverse analysis,comprehensive application of the basic principles of mathematics,choosing the right method,some complex problems will be easily solved.This paper will analyze the characteristics of this kind of problems,summarize the rules,and give several kinds of common question types and common solving methods,to provide a certain theoretical basis for this kind of problems.

关 键 词：方程的根 零点定理 罗尔定理 

分 类 号：O172[理学—数学]