题目

抛物线y=ax2(a＞0)与直线y=kx+b(k≠0)有两个公共点，其横坐标分别是x1、x2,而直线y=kx+b与x轴交点的横坐标是x3,则x1、x2、x3之间的关系是(　　) A.x3=x1+x2                                                                           B. C.x1x3=x1x2+x2x3                                                                D.x1x2=x1x3+x2x3 答案：解法一:(特值法)取a=1,k=1,b=0,则x1=0,x2=1,x3=0, 可排除A、B.再取a=1,k=1,b=1,可得x1+x2=1,x1x2=-1,x3=-1,检验C、D可知D选项适合.解法二:(直接法)把y=kx+b代入y=ax2,得ax2-kx-b=0,x1+x2=,.又,∴x1x2=(x1+x2)x3.答案:D

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