The number a is called a double root of the polynomial function f . 数a称为多项式函数f的二重根。
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Cultural background of an sung jin affair 安重根事件的文化底蕴
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In this paper , it s applications were explained from seven different fields , the common zeros of two polynomials , the multiplicities of roots and the discrimination of a polynomial , searching the equations suitable for a algebraic number , implicating a rational curve over the plane , computing the zeros of a nonlinear algebraic equation and gathering the discrimination surface of the sas in automated theorem proving on inequalities 本文从7个方面阐述了结式的应用，包括判断2个多项式的公共零点，判定多项式是否有重根，计算多项式的判别式，寻找代数数满足的方程，平面有理曲线的隐式化，非线性代数方程组求解和不等式机器证明中半代数系统边界曲面的获得等。
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Through extrapolation , the order is poromted from 2 to 4 . for rannacher - turek element , its single root also gives lower - bound approximation . however , it can reach fourth order and further extrapolation leads to sixth order , while its repeted root has only second order precision and extrapolation leads to fourth order precision 实验结果表明拓广rannacher - turek元确实给出特征值的下逼近，并且要优于线性元，外推可以使2阶精度提高到4阶，而rannacher - turek元对单根同样给出下逼近，但近似解本身便可达到4阶高精度，外推可以获得更高阶( 6阶)精度，重根却给出上逼近，只具有2阶精度，但可以通过外推达到4阶精度。
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Abstract : a conclusion has been proved indelail that only if the na tural frequency k of a symmetric structure is nota duplicate root , the vibra tion mode of the strusture must be symmetrical orantisymmetrical . this conclusio n is advantageous to simplify the structural dynamicanalysis and pratically usef ul 文摘:给出了有关对称结构体系的动力特性的一个结论：对称的结构振动体系，对应于任一非重根的自振频率，其主振型必定是对称的或反对称的.并给出了详细的证明.应用这个结论，有利于对称结构动力分析的简化，具有实用价值
