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一元二次方程的根的判别式在高中数学里是重要的基础知识,在求解含字母系数的一元二次方程的根、二次不等式、二次函数、求函数的值域、求直线与圆锥曲线的相交情况分析等多个章节里有广泛的应用。熟练掌握判别式(△)的各种用法,可以提高同学们的数学解题能力和综合应用能力。但是在应用判别式(△)解决问题时应注意先决条件,不能不加分析地盲目地套用,造成解题错误,或漏解,以下是笔者在教学过程中发现同学们用判别式(△)时极易发生错解或漏解的几类题型。一、一元二次方程类例1已知方程2(k+1)x~2-4kx+3k-2=0有
The discriminant of the root of the quadratic equation is an important basic knowledge in high school mathematics. After solving the root, quadratic inequality, quadratic function and quadratic function of the quadratic equation with letter coefficients, Intersection curve analysis and other chapters have a wide range of applications. Proficiency in discriminant (△) of the various usages, can improve the students’ ability to solve problems in mathematics and comprehensive application ability. However, in the application of discriminant (△) to solve the problem should pay attention to the prerequisites, can not be blindly applied without analysis, resulting in problem-solving errors, or leakage, the following is the author found in the process of teaching students with discriminant (△) When prone to misinterpretation or leakage of several types of questions. First, a quadratic equation Example 1 known equation 2 (k +1) x ~ 2-4kx +3 k-2 = 0 Yes