一元二次方程根的判别式“△”是中学数学学习的重点之一,也是解题的重要工具。它揭示了根与系数之间的内在联系。在解决某些数学问题时,充分发挥判别式“△”的作用,能起到神奇的解题效果。本文仅以“巧用”举例说明。一、利用“△”巧解几何探索题例1如图,AB⊥BC,DC⊥BC,垂足分别为B、C.(1)当AB=4,DC=4时,在线段BC上是否存在点P,使AP⊥PD,如果存在,求线段BP的长;如果不存 Discriminant of root of quadratic equation “△” is one of the focuses of high school mathematics learning and also an important tool for solving problems. It reveals the intrinsic relationship between root and coefficient. In solving some mathematical problems, give full play to the role of discriminant “”, can play a magic effect of solving problems. This article only “clever use ” as an example. First, the use of “△ ” clever geometry to explore Example 1 Figure 1, AB ⊥ BC, DC ⊥ BC, vertical foot were B, C. (1) When AB = 4, DC = 4, If there is a point P, make AP ⊥ PD, if there is, find the length of the line BP. If it does not exist