论文部分内容阅读
一元二次方程的整数根问题难度较大,是中考特别是竞赛中的爬坡题型.本文举例说明与一元二次方程整数根有关问题的解法. 例1 已知方程x2+(α-6)x+α=0(α≠0)的两根都是整数,试求整数α的值. 思路分析:当α取值不同时,方程的系数就随之不同,方程的根的情况也就发生变化.究竟什么情况下,方程的两根都是整数呢?还是从根与系数的关系人手比较好. 解:设方程的两整数根为为x1、x2,根据根与系数关系得
The integer root problem of quadratic equations is more difficult and is a climbing problem in Chinese exams, especially in competitions. This article illustrates the solution to the problems associated with integer roots of a one-dimensional quadratic equation. Example 1 Known equations x2+(α-6) Two of x + α = 0 (α ≠ 0) are integers, try to find the value of the integer α. Thinking analysis: When α is different, the coefficients of the equation will be different, and the root of the equation will also occur. Change. Under what circumstances, the two roots of the equation are all integers? Or the relationship between the root and the coefficient is better. Solution: Let the two integer roots of the equation be x1, x2, according to the relationship between the root and the coefficient.