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关于两个一元二次方程有公根的问题,很多刊物文章都有论述。尤其发表在本刊84年4月号的熊曾润文章,论述得较好,读后受益非浅。但需用到有关行列式的知识,对于初中学生,则无法让其弄懂。而这类题初中已经出现,现将我们在初中处理这类问题的作法,介绍如下,供初中教师及学生参考。一、关于两个方程仅有一个公共根的问题解这类问题步骤如下: 1.首先作差消去二次项,解出公共根表达式(或公根)。 2.把公根表达式(或公根)代入原方程的任一个,求出系数(或关系式)。
With regard to the problem of the common root of the two unary quadratic equations, many publications have discussed them. In particular, Xiong Zengrun’s article, published in the April issue of this issue of the journal, was well-discussed and benefited greatly after reading it. However, knowledge of determinants is needed. For junior high school students, they cannot understand it. The junior high school of this kind has emerged. Now we will introduce the following methods for dealing with such issues in junior high schools for the reference of junior high school teachers and students. First, on the problem that the two equations have only one common root The solution to this type of problem is as follows: 1. First eliminate the quadratic term and solve the common root expression (or public root). 2. Substituting the public root expression (or public root) into any of the original equations, find the coefficient (or relation).