笔者任教高中数学多年,三年一轮,周而复始,有些概念问题在教学中会反复出现。三年前就有一个“一元二次方程根的个数”问题一直没有解决,最近再次遇到,故写就本文,求教于同行,也希望能引起大家对这类问题的关注。1问题提出有一名学生课后提出的问题:例1(2009年全国高中数学联赛第6题)若方程lg kx=21g(x+1)仅有一个实根,那么k的取值范 I teach high school mathematics for many years, three rounds of a week, some of the conceptual problems in teaching will be repeated. Three years ago, there was a question of “the number of roots of a quadratic equation” which has never been solved and has recently been encountered again. Therefore, I wrote this article and sought my advice in the field of peer education. I also hope that it will arouse people’s attention to these issues. Problem 1 Ask a student questions after class: Example 1 If the equation lg kx = 21g (x + 1) has only one real root, then the value of k