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方程问题，历来是中考的重要考点，含参一元二次方程更是屡见不鲜。有些问题看似不难，但若数学概念模糊，掌握知识不够全面，就会产生错误的理解，形成错误的判断，导致错误的结论，从而误入“陷阱”。粗心大意，忽视隐含条件；思维不慎，顾此失彼；受思维定式的影响，以偏概全等都是常见的问题。现就几类常见错例剖析如下，供同学们参考：例1已知关于x的方程kx~2-4x+3=0有实数根，求k的取值范围。错解：∵方程有实数根，∴△=(-4)~2-4k·3≥0，且k≠O，解得k≤4/3，且k≠0。剖析：由于概念不清，忽视了“有实数根”和“有两个实数根”的区别致错。方程“有实数根”包含“有一个实数根”和“有两个实数根”，错解误以
The problem of equations has always been an important test point for the entrance examination, and the inclusion of a one-dimensional quadratic equation is not uncommon. Some problems do not seem difficult, but if the concept of mathematics is ambiguous and knowledge is not comprehensive enough, it will lead to misunderstandings, wrong judgments, and erroneous conclusions, thus straying into the “trap.” Carelessness, neglect of implied conditions, careless thinking, and disregard for each other; being influenced by thinking patterns are all common problems. Here are some common examples of mistakes that are discussed below for reference by students: Example 1 Given that the equation kx~2-4x+3=0 for x has a real number root, find the range of values for k. Misunderstanding: The ∵ equation has a real root, ∴ △ = (-4) ~ 2-4k 3 3 ≥ 0, and k ≠ 0, the solution k ≤ 4/3, and k ≠ 0. Analysis: As the concept is unclear, we ignore the difference between “having a real number root” and “having two real number roots”. The equation “has a real number root” contains “has a real number root” and “has two real number roots”, misinterpreting false positives