众所周知,实系数一元二次方程ax~2+bx+c=0(a≠0)的判别式是:Δ=b~2-4ac,当Δ>0时,方程有两个不相等的实数根;当Δ=0时,方程有两个相等的实数根;当Δ<0时,方程没有实数根。对于以上的结论,在代数、几何、三角的解题中都有广泛的应用。如果我们经常注意这类问题的解法,并在课堂上广为介绍,则有利于数学知识的相互沟通,还有利于理论联系实际,更有利于提高学生分析问题和解决问题的能力。兹将一元二次方程根的判别式的应用,整理归纳如下,以供同志们参考。 1.用于讨论方程的根的性质 It is well known that the discriminant of the real coefficient quadratic equation ax ~ 2 + bx + c = 0 (a ≠ 0) is: Δ = b ~ 2-4ac. When Δ> 0, the equation has two real numbers ; When Δ = 0, the equation has two equal real roots; when Δ <0, there is no real root in the equation. For the above conclusion, in algebra, geometry, the triangular problem has a wide range of applications. If we often pay attention to the solution of such problems and introduce them widely in the classroom, it is conducive to the mutual communication of mathematical knowledge, but also conducive to combining theory with practice, and more conducive to improving students' ability to analyze and solve problems. This will be one yuan quadratic equations of the discriminant application, summarized as follows, for the comrades for reference. 1. The nature of the root used to discuss the equation