判别式法是一种重要的数学方法,对于某些问题,根据题目特点,在解题过程中可以反复运用判别式,达到快速解题的目的.例1已知函数y=(ax+b)/(x~2+1)的值域为[-1,4],求a,b的值.分析这类问题通常的解法是,首先确定函数的定义域为R,再将式子整理成关于x的一元二次方程yx~2-ax+y-b=0,然后根据该方程有实数解,得Δ=a~2-4y(y-b)≥0,由题意知-1,4 Discriminant method is an important mathematical method, for some problems, according to the characteristics of the subject, in the process of solving problems can repeatedly use discriminant, to achieve rapid solving the problem. Example 1 Known function y = (ax + b) / (x ~ 2 + 1) is [-1,4], find the values ​​of a and b.A typical solution to this kind of problem is to first determine the domain of the function as R and then arrange the formula into On the quadratic equation of x yx ~ 2-ax + yb = 0, and then the real solution of the equation, we have Δ = a ~ 2-4y (yb) ≥ 0,