多项式的根的分布问题数学专业论文设计VIP专享

摘 要本文主要考虑多项式的正根、负根的个数问题，通过介绍多项式的相关定理及符号原则，并举出实例，总结整理多项式的根的分布问题，把多项式的根的分布问题进行细致归纳． 关键字：多项式；存在性；二分法；根I ABSTRACTThis paper mainly considers the number of positive and negative roots of polynomials ． By introducing the relatrd theorems and sign principles of polynomials，and gives examples．Summarizes and sorts out the root distribution of polynomials，and sums up the root distribution of polynomials in detail．Keywords：polynomial；exist；dichotomy；rootII 目录摘 要.................................................................................................................IABSTRACT...........................................................................................................II第 1 章 绪论....................................................................................................1第 2 章 多项式根的存在性.........................................................................22．1相关定理介绍..................................................................................22．2例题总结..........................................................................................2第 3 章 多项式的根的确定性....................................................................43．1奇次多项式的根的确定性...............................................................43．2偶次多项式的根的确定性...............................................................4第 4 章 笛卡尔符号原则.............................................................................94．1多项式的正根................................................................................104．2多项式的负根................................................................................10第 5 章 总结..................................................................................................12参考文献......................................