题目

已知a，bR且ab≠0，若(x–a)(x–b)(x–2a–b)≥0在x≥0上恒成立，则（    ） A. a<0                               B. a>0                               C. b<0                               D. b>0 答案：C 【解析】 【分析】 对分与两种情况讨论，结合三次函数的性质分析即可得到答案. 【详解】因为，所以且，设，则的零点 为 当时，则，，要使，必有，且， 即，且，所以； 当时，则，，要使，必有. 综上一定有. 故选：C 【点晴】本题主要考查三次函数在给定区间上恒成立问题，考查学生分类讨论思A young man once went into town and bought himself a pair of trousers. When he got home, he went upstairs to his bedroom and put them on. He found that they were about two inches (英尺) longer.He went downstairs to the kitchen. His mother and two sisters were washing up the tea-things there. “The new trousers are too long,” he said. “They need shortening（缩短）by about two inches. Could one of you do it for me, please?” His mother and sisters were busy and none of them said anything. But when his mother  finished washing up, she went quietly upstairs to her son’s bedroom and shortened the trousers by two inches. She came downstairs without saying anything to her daughters. Later on, after supper, the elder sister remembered her brother’ s trousers. She was a kind girl,so she went quietly upstairs withoutsaying anything to anyone, and shortened the trousers by two inches.  The younger sister went to the cinema, but when she came home she,too, remembered her brothers trousers. So she ran upstairs and did as her mother and sister had done. You can imagine（想象）the look on the young man’s face when he put the trousers on the   next morning.   .1.What were the young man’s new trousers like at first? A.They were a bit too long.B.They were just suitable.C.They were too short for him.D.There were about two inches shorter.2.Why didn’t the young man’s mother and sisters answer him in the kitchen? A.Because they were very busy.B.Because they didn’t hear him.C.Because they didn’t like him.D.Because they couldn’t do that.3.When did his elder sister shortened the trousers? A.In the evening.B.Before she finished the washing.C.After lunch.D.After she came back from the cinema.4.What did the young man find about the trousers the next morning?He found that the trousers were ______ inches too short for him. A.twoB.fourC.sixD.eight5.How did the young man feel when he put the trousers on the next morning? A.Pleasant.B.Thankful.C.Surprised.D.Bored.