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一元二次方程问题中,往往有一些容易被忽视的条件隐含其中,解题时若忽视这些隐含条件,则可导致错解.本文列举并剖析此类问题中的常见错解,希望引起大家的注意. 一、用判别式解题时忽视二次项系数不为零 例1 已知关于x的一元二次方程(m+2)x2+2x-1=0有两个不相等的实数根,求m的取值范围. (2000年云南省中考题) 锗解由题意得△=22-4(m+2)·(-1)>0,∴m>-3. 剖析本题错在只考虑方程有两个不相
In the problem of quadratic equations, there are often conditions that are easily overlooked. However, if these implicit conditions are ignored when solving a problem, it can lead to misinterpretation. This article lists and analyzes common misconceptions in such problems, and hopes to Everyone’s attention. I. Ignoring quadratic terms when solving problems with discriminant equations is not zero. Example 1 It is known that the quadratic equation (m+2)x2+2x-1=0 for x has two unequal real numbers. Root, find the value of m range. (Yunnan Province in 2000, the examination questions) solve the problem by the meaning of △ = 22-4 (m +2) (-1)> 0, ∴ m> -3. Analysis of the wrong title There are only two inconsistencies in considering the equation