摘要韦达定理对于数学的研究者来说再熟悉不过了，包括其表现形式，本文首先先简述了什么是韦达定理，并用数学语言表示了韦达定理，进而再将韦达定理推广到了一般的方程。阐述完什么是韦达定理之后，本文从韦达定理的发展历史做了简单的介绍，最早是我国伟大的数学家赵君卿研究发现这一规律，但是是韦达最早系统的引入符号，并用符号简明的阐述了一元二次方程根与系数的关系。韦达定理的发展从最开始仅局限于正数根到后面扩展到实数根，到最后的复数根，荷兰数学家吉拉尔作出了卓越的贡献。但是韦达定理作为新课标中为选学内容，因此在中学数学教学过程中大部分教师对本课不重视，大部分教师跳过这节课，或者只是简单的进行讲解。韦达定理遭到师生的冷落，并不深入人心。本文重点研究了韦达定理的应用，主要是韦达定理在解一元高次方程中应用、韦达定理在平面解析几何中应用、韦达定求几类典型代数式值中应用。在探究解一元高次方程中应用，先研究一元四次方程应用韦达定理的条件：即对于方程 能使用韦达定理求解必须满足 。有了一元四次方程的经验之后，再模仿一元四次方程研究推广到一元 次方程中韦达定理应用的条件。韦达定理在平面解析几何中应用中主要是求相交弦的中点坐标，相交弦的长，圆锥曲线的最值问题，以实例来分析如何应用韦达定理来解这几类题目。韦达定理求代数式的值中的应用则是通过如何变化 这些式子使得这些式子与韦达定理产生联系，从而将两根之和与两根之积的值代入已经变化好的式子得出我们所要求的代数式的值最后从教师的角度谈谈韦达定理对学生的意义，韦达定理有利于学生计算能力的发展、模型思想的发展、创新意识的发展、推理能力的发展，而这些能力正是当代学生着重该培养的一些能力，忽视韦达定理的教学，学生的这些方面能力发展不足，值得作为教师的我们反思。88921

毕业论文关键词;  韦达定理  应用  学生发展

Abstract Wiete's theorem is familiar to the researchers of mathematics, including its manifestations。 This paper first briefly describes what is the Veda theorem and expresses the Wiete's theorem in mathematical language, and then generalizes the Veda theorem to the general The equation。 After the elaboration of what is the Wiete's theorem, this article from the development of the Wiete's theorem made a simple introduction, the first is China's great mathematician Zhao Junqing study found this law, but the first system of the introduction of Wiete's symbols, and symbolic concise The relationship between the root and the coefficient of the quadratic equation is expounded。 The development of the Wiete's theorem from the beginning was confined to the positive roots to the back to the real roots, to the final plural roots, the Dutch mathematician Girard made an outstanding contribution。 But the Wiete's theorem as the new curriculum for the selection of content, so in the middle school mathematics teaching process, most teachers do not attach importance to this lesson, most teachers skip this lesson, or simply explain the Veda theorem Teachers and students of the cold, not deeply rooted。 In this paper, we focus on the application of Wiete's theorem, mainly the application of Vader's theorem in the solution of plane-solving geometry, and the application of several kinds of typical algebra。 In the study of the solution of the solution of a high order equation, we first study the condition of applying the Vader's theorem to the quadratic equation: that is , the equation can be solved by using the Vader's theorem 。 With the experience of the equation, we then mimic the condition of the application of the quadratic equation to the application of the Vader's theorem in the first-order equation。 In geometric applications, we mainly want to find the midpoint coordinates of intersecting strings, the longest intersecting string, the most problem of conic curve, and the example to analyze how to apply Viete's theorem to solve  these problems。 The application of these formulas makes these formulas in contact with the Vader's theorem。源Q于D优G尔X论V文Y网wwW.yOueRw.com 原文+QQ75201`8766 韦达定理及其恒等式:http://www.youerw.com/shuxue/lunwen_171644.html