有关一元二次方程的整数根问题是近些年来数学竞赛中常出现的一种题型,也是中考的一种新趋向,要解决这类问题,必须学习好一元二次方程的基础知识,掌握整数、完全平方数的性质,结合分类讨论等数学思想,选择合适有效的解题方法.现举例说明解决这类问题的一些常用方法与思路。 一、因式分解法 对于整理成一般形式的一元二次方程,如果方程左边的二次三项式能因式分解(如十字 The question of the integer root of the quadratic equation is a new type of question that often appears in mathematics competitions in recent years. It is also a new trend in the examination. To solve this kind of problem, we must learn the basics of the quadratic equation of one yuan and master the integers. The nature of the complete square number, combined with mathematical thinking such as classification and discussion, select the appropriate and effective method of solving the problem. Here are some common methods and ideas for solving such problems. First, the factorization method For the unary quadratic equation organized into a general form, if the quadratic trinomial on the left side of the equation can be factorized (like a cross