一元二次方程中根的判别式的应用是十分广泛的,下面就其主要应用作一介绍.一、根据判别式的符号,判断根的情况例1证明对于任意实数K,方程x~2-(k+1)x+k=0有实根.证明方程x~2-(k+1)x+k=0根的判别式为△=[-(k+1)]~2-4k=k~2-2k+1=(k-1)~2不论k取何值,(k-1)~2≥0,即△≥0.所以不论k取何值,方程x~2-(k+1)x+k=0均有实根.例2若关于x的方程x~2+px+q=0有相等的实 The application of the discriminant in the root of a quadratic equation is very broad, the following is a brief introduction of its main application. First, judge the root situation according to the sign of discriminant Example 1 proves that for any real number K, the equation x ~ 2- ( k + 1) x + k = 0, and the discriminant of the root of the equation x ~ 2- (k + 1) x + k = 0 is proved to be △ = [- (k + 1)] ~ 2-4k = k ~ 2k + 1 = (k-1) ~ 2 Regardless of the value of k, (k-1) ~ 2≥0, that is △ ≥ 0. Therefore, whatever the value of k, 1) x + k = 0 Example 2 If the equation x ~ 2 + px + q = 0 for x has an equal real