一、求根法用分解因式法表示出一元二次方程的两个解,再利用约数的特性及根据题意解决此类问题·例1已知方程a2x2-(4a2-5a)x+3a2-9a+6=0(a为非负整数)至少有一个整数根,那么a=·解:原方程变形,得[ax-(3a-3)][ax-(a-2)]=0,所以ax=3a-3或ax=a-2·因为a为非负整数,所以x1=3aa-3=3- First, the root method uses the decomposition factor method to express the two solutions of the one-dimensional quadratic equation, and then uses the characteristics of the divisor and solves the problem according to the problem. Example 1 Known equation a2x2-(4a2-5a)x+ 3a2-9a+6=0 (a is a non-negative integer) has at least one integer root, then a = · solution: the original equation deformation, get [ax-(3a-3)][ax-(a-2)] = 0, so ax=3a-3 or ax=a-2. Since a is a non-negative integer, x1=3aa-3=3-