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一元二次方程根的分布问题是高中数学的一个重点,也是一个难点。许多学生在解决这类问题时,分很多种情况进行讨论,这种讨论过于繁琐,而且很容易出错。其实,深入研究这类题目,就会发现,它是有规律的。通常,遇到一元二次方程根的分布问题,首先数形结合,画出相应的函数图像,然后判断两根是分布在同一区间还是两个区间里:1若分布在两个区间,则只需考虑抛物线的开口方向和区间端点所对应的函数值的正负;2若分布在同一区间,则考虑两个
The distribution of roots of quadratic equations is one of the focuses of high school mathematics, but also a difficult point. Many students discuss this type of issue in many different situations. Such discussions are too complicated and error-prone. In fact, in-depth study of such topics, you will find that it is regular. Usually, we encounter the problem of distribution of roots of quadratic equations. First, we combine several figures to draw the corresponding function image, then judge whether two are distributed in the same interval or two intervals: 1 if distributed in two intervals, only Need to consider the opening direction of the parabola and the end of the interval corresponding to the positive and negative function values; 2 if distributed in the same interval, consider two