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关于x的整系数方程ax2+bx+c=0(a≠ 0)的整数根问题,常常是中考和数学竞赛命题 的重要内容．这类问题涉及面广,综合性强,除 要应用判别式和根与系数的关系,还要应用整 数的有关性质．本文以全国初中数学联赛试题 介绍利用两数和(a+b)与两数积ab构造(a± 1)(b±1)解一类有关整数根的竞赛题．
The integer root problem of the integer coefficient equation ax2+bx+c=0(a≠ 0) for x is often an important part of the propositions of the Chinese exam and math contest. This type of problem involves a wide range of issues and has a strong comprehensive nature. In addition to the application of discriminants and the relationship between roots and coefficients, the relevant properties of integers must also be applied. In this paper, the national junior high school mathematics league questions are introduced to use the two-sum (a+b) and two-number product ab construct (a±1)(b±1) to solve a class of contests involving integer roots.