一元二次方程根的类型多样,其中不乏“特殊”根.抓住并利用“特殊”根呈现出的某种特征,是解决相关问题的有效方法.一、有理根对于系数是有理数的一元二次方程ax~2+bx+c=0(a≠0,b~2-4ac≥0),b~2-4ac是完全平方数方程两根是有理数.例1m为有理数,求k为何值时,方程x~2+4(1-m)x+3m~2-2m+ There are many types of roots in the quadratic equation, and there is no shortage of “special ” roots. Grasping and using a certain characteristic of the “special ” root is an effective way to solve the related problems. The rational quadratic equation ax ~ 2 + bx + c = 0 (a ≠ 0, b ~ 2-4ac ≥ 0), b ~ 2-4ac is the square equation of the two rational numbers. When k is the value, the equation x ~ 2 + 4 (1-m) x + 3m ~ 2-2m +