一元二次方程实根分布问题是中学数学的一种重要题型，解决它的一般方法是“抛物线法”，即利用抛物线与ｘ轴交点的位置来确定一元二次方程在给定区间内有实根的充要条件．这是一种较好的通法，但学生在实际应用该法解决上述问题时，常感到讨论过复杂、易遗漏、且在解不等式时 The real root distribution problem of one-level quadratic equation is an important problem in middle school mathematics. The general method to solve it is “parabolic method”, which uses the position of parabola and x-axis intersection to determine the quadratic equation in a given interval. The necessary and sufficient conditions for real roots. This is a good general method, but when students actually apply this method to solve the above problems, they often feel that the discussion is complicated, easy to miss, and when solving inequality