我们知道一元二次方程ax~2+bx+c=0(a≠0)根的判别式△=b~2-4ac与方程的根有下列等价关系: △>0:方程有两个不相等的实数根; △=0:方程有两个相等的实数根; △<0:方程没有实数根。 这种关系,在解题中应用非常广泛,本文从以下几个方面做以总结: 1.判断一元二次方程根的情况 We know that the discriminant △ = b ~ 2-4ac of the root of the quadratic equation ax ~ 2 + bx + c = 0 (a ≠ 0) has the following equivalence relation with the root of the equation: Δ> 0: Equal real roots; △ = 0: Equations have two equal real roots; △ <0: Equations do not have real roots. This relationship, which is widely used in problem solving, is summarized in the following aspects: 1. Judging the condition of the root of a quadratic equation