△ =b2 - 4ac叫做一元二次方程 ax2 + bx+ c=0(a≠ 0 )的根的判别式。灵活应用它 ,不仅可以解答一些与一元二次方程有关的问题 ,一些非一元二次方程问题也可获得巧妙解答。一、与一元二次方程有关的问题例 1　若方程 x2 - (a- 3) x- 3a- b2 =0有两个等根 ,则方程 x2 + ax+ b=0 △ = b2 - 4ac is the discriminant of the root of a quadratic equation ax2 + bx + c = 0 (a ≠ 0). The flexible application of it can not only solve some problems related to the unary quadratic equation, but also solve some non-unique quadratic equation problems. First, problems related to the unary quadratic equation Example 1 If the equation x2 - (a - 3) x - 3a - b2 =0 has two equal roots, the equation x2 + ax + b = 0