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二次方程之根的分布及个数,可经过计算求出,但学生往往因考虑问题不全面会产生遗漏,通过复合幻灯片,多方位地引导学生观察,寻找规律,可引起兴趣,使其条理分明,迅速地解题。例1 k为何值,7x~2-(k+13)x+k~2-k-2=0两根分别在(0,1)与(1,2)之内。 [投影演示] 图1,抛物线与横轴交点A、B在于(0,1)、(1,2)之间。解:设f(x)=7x~2-(k+13)x+k~2-k-2,从图象可以看出:
The distribution and the number of roots of the quadratic equations can be calculated and calculated. However, students often miss the problem by considering the incompleteness of the problem. Through composite slides, students can be guided to observe in multiple directions and find laws, which can cause interest. Clearly and quickly solve the problem. What is the value of the case 1k, and 7x~2-(k+13)x+k~2-k-2=0 are respectively within (0,1) and (1,2). [projection demonstration] Figure 1, the intersection of the parabola and the horizontal axis A, B lies between (0,1), (1,2). Solution: Let f(x)=7x~2-(k+13)x+k~2-k-2, as can be seen from the image: