一、题目呈现(2016年全国课标卷Ⅰ)已知函数f(x)=(x-2)e~x+a(x-1)~2有两个零点.(1)求a的取值范围;(2)设x1,x2是f(x)的两个零点,证明:x_1+x_2<2.二、试题解析1.第(1)问的分析与解答第(1)问由函数零点个数确定参数的取值范围,我们可以采用分类讨论,结合零点存在性定理求解;也可以采用参变量分离,数形结合的方法加以解决,这两种方法都是通性通法. First, the title is presented (2016 National Curriculum I) known function f (x) = (x-2) e ~ x + a (x-1) ~ 2 has two zero points. (2) Suppose x1 and x2 are two zero points of f (x), and prove that: x_1 + x_2 <2. 2. Analysis of Questions 1. Analysis and Solution of Question (1) Question (1) The number of zero points determines the range of parameters, we can use the classification discussion, combined with the zero existence theorem to solve; also can be used by the variable separation, the combination of number form to be solved, these two methods are generalized method.