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对于含有某一参数的三次方程,若已知方程根的个数,则可确定参数的取值范围;若已知参数的取值范围,则可确定方程根的个数.对这类问题的解答方法很多,下面从两方面以含有参数的三次方程问题为例进行分析.1.由方程中某一实数的取值范围,求方程根的个数对方程所对应的函数求导数,由此求出两个极值,利用x轴在两个极值所分成三个区间中的位置关系和参数的取值范围求出方程根的个数.例1设a>3,判断方程x3-ax2+1=0在
For a cubic equation containing a certain parameter, if the number of the root of the equation is known, the range of the parameter can be determined; if the range of the parameter is known, the number of the root of the equation can be determined. There are many ways to solve the problem, the following two aspects of the problem with the cubic equation containing the parameters as an example for analysis.From the range of a real number in the equation, find the number of root of the equation of the function corresponding to the equation to find the derivative, thus Find two extreme values, the use of the x-axis in the two extremum divided into three intervals and the value of the relationship between the range of parameters to find the number of root equation Example 1 Let a> 3, to determine the equation x3-ax2 + 1 = 0 in