当a＞0时，函数f（x）=ax+
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证明：假设f（x）=0 有负根 x0，且 x0≠-1，即 f（x0）=0．
根据f（0）=1+
=-1，可得 f（x0）＞f（0）①． 0-2 1+0
若-1＜x0＜0，由函数f（x）=ax+
在（-1，+∞）是增函数，可得f（x0）＜f（0）=-1，这与①矛盾．x-2 x+1
若x0＜-1，则 ax0＞0，x0-2＜0，x0+1＜0，∴f（x0）＞0，这也与①矛盾．
故假设不正确．∴方程 ax+
=0 没有负根．x-2 x+1
 Two teachers were sitting in the teachers' room. For a moment there was silence. Then one of them, Miss Smith, said, "I'm afraid I'd have to fail him! I just can’t let him 16 . " "Now Alice," said her friend, Mrs Jackson, "is he so terrible a student?" "That's just the trouble!" the other woman answered, "Tom was ever my 17 student. The problem is that he is so lazy that he never gets his work done. He hasn't handed me a piece of homework for three 18 !" Mrs Jackson had never seen Miss Smith so 19 before. "Have you had a word with him about it?" she asked. "Why should I? Every student must hand in homework. I made 20 very clear on the first day for class. I don't know what has happened. When the lessons started, he did so well that I 21 thought about asking the school to give him a scholarship(奖学金). But now he often sleeps in class! I've never seen such a 22 in a student." "You should have a talk with him. Give him a chance. " Miss Smith spoke to Tom and learned all about it. He was studying all day and working most of the night in a factory to 23 for his schooling. Of course he was 24 in class and sometimes could hardly 25 awake. Miss Smith soon asked the school to give him a scholarship and he was able to devote himself to his lessons again.
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