再论实数型多项式方程进行根式求解的条件
首发时间:2019-09-24
摘要:这篇文章专题研究了由两个多项式函数的代数和所定义方程中,因两个函数的常数项在非线性空间作用下相互抵消提取的一次公因式与这两个本源方程公根锁定的交点的关系。证明了这个公因式定义的方程求出的根与两个本原方程的公根无关。如果把对给定多项式方程进行因式分解的目的理解为求这两个本原方程的公根,就完成了上述交点分解式根域的定义工作。以此为依据探讨了与给定方程方程等价的参数方程进行线性代换时,利用线性代换因子和参数结构的共同作用消除这个参数方程坐标平移表达式中常数项的可行性。介绍了由给定方程系数的参数表达式和两个相交函数的幂零条件锁定参数结构中各参数取值的方法。文章应用数学归纳法第二原理证明了任何给定的三阶以上多项式方程均可在系数参数化的条件下利用线性代换的方式消去常数项后进行因式分解。通过一元三次多项式方程根域形式的探讨证明了多项式函数进行因式分解的形式和因式分解的路径有关。只要特征参数值选择合理,用系数参数化消常法求出的给定方程交点分解式的根域甚至可保持在实数域内。
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Re-discussion on the Conditions for Solving the Roots of Polynomial Equations
Abstract:In this paperthe relationship between common factors that is extracted from sum ofand two functions when the constant terms of these two functions cancel each other out and intersection points of intersecting functions is specially studied.It is proved that these roots which is derived from the common factor of the equation are independent of the common roots of two source equations.If this is the purpose of factorization of a given equation in order to solve the common roots of two primitive equations ,The root field of this intersection decomposition completes the definition.The feasibility of eliminating the constant expression of this parametric equation which is equivalent to the given equation is studied when the parametric equation is linearly substituted by using to .The method of locking parameters in the parameter structure is introduced by using parametric expressions of two coefficients of a given equation and nilpotent conditions for two Intersecting functions.It is proved by the Second Principle of Applied Mathematical Induction that the parameterized polynomial equation of more than three times can be factorized after the constant terms of the equation cancel each other out .After discussioning on the form of root domain of cubic polynomial equation ,this principle has been proved that the factorization form of polynomial equation is related to the path of factorization.If the eigenvalues are selected reasonably, the root field of the intersection decomposition can be maintained in the real field after the coefficients of the equation are parameterized and the constant terms of the equation
Keywords: polynomial linear transformation field radical solution vector space
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