一元二次方程实根的分布问题,是初等代数中研究的核心内容,而分类讨论、数形结合等是高考试题的重要的数学思想方法.所以,在教学中,既要有正确的结论和方法,也不妨提供一些笨拙的,甚至是错误的推断和方法,让学生走一些弯路,在教与学的过程中,逐步养成严谨求实、一丝不苟的科学态度. The distribution of real roots of quadratic equations is the core of research in elementary algebras. Classification discussion and combination of number and shape are important mathematical thinking methods for high test questions. Therefore, in teaching, it is necessary to have correct conclusions and The method may also provide clumsy or even erroneous inferences and methods to allow students to take some detours and gradually develop a rigorous, realistic and meticulous scientific attitude in the teaching and learning process.