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有关一元二次方程根的问题,既是初中数学的重点,也是各地中考的热点。而根的判别式在一元二次方程的解题中有具有极其重要的地位。其主要用途有两个方面:一是不用解方程,根据判别式的值判断方程的实数根的情况;二是根据方程有无实数根的情况(通常涉及到根与系数的关系)确定方程中某一待定系数的取值范围。如果二次项系数中含有字母时,要特别注意加上二次项系数不为零这一限制条件。
The problem of roots of quadratic equations of one yuan is not only the focus of junior middle school mathematics, but also the hot spot of the examinations in various places. The discriminant of root has an extremely important position in solving the quadratic equation. Its main purpose has two aspects: First, do not understand the equation, according to the value of the discriminant to determine the real root of the equation; Second, according to the equation with or without real roots (usually related to the relationship between root and coefficient) to determine the equation The range of a certain coefficient to be determined. If the quadratic coefficients contain letters, pay special attention to the constraint that the quadratic coefficient is not zero.