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教育部在中考改革的《指导意见》中指出:数学考试“应设计一定的结合现实情境的问题和开放性问题”。开放题具有答案不唯一的特征,它有利于考生发挥创新能力.因此,开放题受到普遍重视,成了各地数学中考试卷中的重要新题型.例1(江西2004年)已知关于x的方程x2-2(m+1)+m2=0.(1)当m取什么值时,原方程没有实数根;(2)对m选取一个合适的非零整数,使原方程有两个实数根,并求这两个实数根的平方和.分析(1)当△<0时,方程没有实数根,可求得m<-1/2(2)要使方程有实数根,必须要有△≥0,由(1)即知须有m≥-1/2.但要取非零整数m故,m可选1或2等正整数.
The Ministry of Education pointed out in the “Guiding Opinions” of the reform of the Chinese exam: The math exam “should be designed with a certain combination of realistic situations and open issues.” The open question has the unique feature of the answer, which is conducive to the candidate’s ability to innovate. Therefore, the open question has received universal attention and has become an important new question in the mathematics test in various regions. Example 1 (Jiangxi 2004) Known about x Equation x2-2(m+1)+m2=0. (1) When m takes any value, the original equation has no real root; (2) Select an appropriate non-zero integer for m, so that the original equation has two real numbers Root, and find the sum of the squares of the two real numbers. Analysis (1) When △ <0, the equation has no real number roots, can be obtained m <- 1/2 (2) To make the equation have real roots, must have △ ≥ 0, from (1) that knowledge must be m ≥ - 1/2. But to take a non-zero integer m, m can choose 1 or 2 positive integers.