题目

已知a、b、c均为实数,证明ac＜0是关于x的方程ax2+bx+c=0有一正根和一负根的充要条件. 答案：思路分析：由一元二次方程判别式及根与系数的关系式可得.证明:(1)充分性:若ac＜0,则Δ=b2-4ac＞0.∴方程ax2+bx+c=0有两个相异的实根.设为x1、x2.∵ac＜0,∴x1·x2=,即x1、x2的符号相反,方程有一个正根和一个负根.(2)必要性:若方程ax2+bx+c=0有一个正根和一个负根,则设为x1、x2.不妨再设x1＜0,x2＞0,则x1x2=,∴ac＜0.由(1)( 冲刺突破三十七篇 语法填空（每篇共10小题; 每小题1.5分，满分15分） 阅读下面短文，按照句子结构的语法性和下文连贯的要求，在空格处填入适当的词 或使用括号中词语的正确形式填空，并将答案填写在答题卡标号为31~40 的相应位置上。 Many people like to read the (31) ___________________（late）newspapers. But  (32) _______________ is it produced so quickly? The most important man may be the chief editor. He decides (33) ______________ to do. Every morning the (34)________________ (journal) are sent to cover the events. Sometimes they need a face-to-face interview with people (35) _____________ do telephone interviews. Meanwhile, the picture editor sends (36) _______________ (photograph) to take the pictures they need. Later in the day, they pass the stories and the (37)_________________ (develop) photos to the editor. Then the chief editor will choose the most important news for the front page. (38)_________________ editors read the stories, make some necessary changes and write headlines for them. (39)__________________ the newspaper is printed and (40)_________________（deliver）to different places.