二次方程的判别式只能判定根的虚实和异同,通过相应的二次函数的图象却能直观地确定根的分布情况,现举例说明如下.例1关于x的二次:亏程丫+2(k+3)x+Zk+4二0两个实根一个大于3,一个小于3,求k的范围. 二次函数f(x)二分+2(k+3)x+2庵+4的图象如图l所示,易见,城使x,<3(均,只要f(3)= The discriminant of the quadratic equation can only determine the difference and similarity of the roots. The distribution of the roots can be determined intuitively through the image of the corresponding quadratic function. Here is an example of the following. Example 1 Quadratic on x: Loss +2(k+3)x+Zk+4 Two zeros Two real roots One greater than 3, one less than 3, find the range of k. Quadratic function f(x) bis 2 + k(k + 3) x + 2 The image of +4 is shown in Fig. 1, easy to see, the city makes x, <3 (all, as long as f(3) =