20xx年畢業(yè)論文韋達(dá)定理的推廣及若干應(yīng)用(已修改)
2025-06-06 00:48 本頁面
【正文】 本科畢業(yè)論文 題 目 : 韋達(dá)定理的推廣及若干應(yīng)用 院 系 ： 數(shù)學(xué)與信息科學(xué)學(xué)院 專 業(yè) ： 數(shù)學(xué)與應(yīng)用數(shù)學(xué) 姓 名 ： 張金顯 學(xué) 號(hào) ： 090501401012 指導(dǎo)教師 ： 王 琪 教師職稱 ： 副教授 填 寫 日期： 20xx 年 5 月 2 日 貴陽學(xué)院畢業(yè)論文 I 摘 要 初等代數(shù)是研究數(shù)學(xué)的代數(shù)運(yùn)算的理論和方法，比如，研究實(shí)數(shù)和復(fù)數(shù)，以及以它們?yōu)橄禂?shù)的多項(xiàng)式的代數(shù)運(yùn)算理論和方法的數(shù)學(xué)分支學(xué)科 .初等代數(shù)研究主要的內(nèi)容是解方程，因而長(zhǎng)期以來都把代數(shù)學(xué)理解成方程的科學(xué) .高等代數(shù) 在初等代數(shù)的基礎(chǔ)上進(jìn)一步 擴(kuò)充研究對(duì)象和研究范圍 ，從最簡(jiǎn)單的一元二次方程開始，更深層的繼續(xù)討論三次、四次方程以及高次方程，探索一元高次方程的求解方法 . 韋達(dá)定理是初等代數(shù)中最重要的內(nèi)容之一，它揭示了一元二次方程中根與系數(shù)的基本關(guān)系 .本文將從韋達(dá)定理在一元二次方程中的簡(jiǎn)單應(yīng)用，初步討論一 元二次方程根與系數(shù)的基本關(guān)系，然后利用高等代數(shù)中的多項(xiàng)式理論將其推廣到一元高次方程中，重點(diǎn)討論一元 高 次方程中根與系數(shù)的關(guān)系，并介紹它在數(shù)學(xué)中的若干應(yīng)用 . 關(guān)鍵詞 ： 代數(shù)方程； 初等數(shù)學(xué)；韋達(dá)定理的推廣；根與系數(shù)的關(guān)系；韋達(dá)定理 貴陽學(xué)院畢業(yè)論文 II Abstract Elementary algebra is the theory and method that studies the algebraic operation of mathematics. For example, it studies the real number and the plex number, as well as the mathematics branch discipline of the theory and method of the polynomial algebraic operation that takes the real number and plex number as the coefficient. The main content of the Elementary algebra research is to solve equation and thus algebra has been interpreted as the science of equations for a long time. Advanced algebra in the elementary algebra on the basis of the further expansion of the research object and research scope. Starting from quadratic equation that is the most simple, deeper continues to discuss three, four equations and equations of higher, and explores the solution method of highorder equations method with one unknown. Veda’s theorem is one of the most important elements in the Elementary in the Elementary Algebra and it reveals the basic relations between the root and the coefficient in quadratic equation with one unknown. From the simple application of the Veda’s theorem in quadratic equation, this article will preliminarily discuss the relationship between the root and the coefficient of quadratic equation, and then promotes it highorder polynomial equation by using the polynomial theory in higher algebra. It focuses on the discussion of the relationship between the root and coefficient of equation with highorder polynomial equation, induction the general form of Veda’s theorem in the equation with one unknown, finally introduced several applications in some areas of mathematics. Keywords: Algebraic equation。 Elementary Mathematics。 The promotion of Veda’s theorem。 Relationship between the roots and coefficients。 Veda’s theorem。 貴陽學(xué)院畢業(yè)論文 III 目 錄 摘 要 ..................................................................................................................................... I Abstract ..................................................................................................................................II 第一章 前言 ......................................................................................................................... 1 第二章 韋達(dá)定理概述及簡(jiǎn)單應(yīng)用 ..................................................................................... 2
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