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一元二次方程是初中数学的主要内容之一,是中考的一个必考内容.同学们在解题时,由于考虑问题不全面,思维不严谨,常会出现这样或那样的错误.现举例分析,供参考. 一、忽视一元二次方程中二次项系数a≠0造成错误例1 (2001年济南市)已知关于x的方程k2x2+(2k-1)x+1=0有两个不相等的实数根x1、x2,求k的取值范围. 错解:∵方程有两个不相等的实数根, ∴原方程为一元二次方程且△>0, 即(2k-1)2-4k2>0,
The one-dimensional quadratic equation is one of the main contents of junior high school mathematics, and it is a must-read content for the middle school entrance examination. When students solve problems, due to the incompleteness of thinking and rigorous thinking, one or more errors often occur. Examples are now analyzed. For reference, I. Ignoring the quadratic coefficient of a quadratic equation a≠0 causes an error. Example 1 (Jinan, 2001) It is known that the equation k2x2+(2k-1)x+1=0 for x has two inequalities. The real roots x1, x2, find the range of k. The wrong solution: the ∵ equation has two unequal real roots, the ∴ equation is a quadratic equation and △> 0, ie (2k-1) 2-4k2 >0,