29、閱讀下列內(nèi)容后,解答下列各題:幾個(gè)不等于0的數(shù)相乘,積的符號(hào)由負(fù)因數(shù)的個(gè)數(shù)決定.
例如:考查代數(shù)式(x-1)(x-2)的值與0的大小
當(dāng)x<1時(shí),x-1<0,x-2<0,∴(x-1)(x-2)>0
當(dāng)1<x<2時(shí),x-1>0,x-2<0,∴(x-1)(x-2)<0
當(dāng)x>2時(shí),x-1>0,x-2>0,∴(x-1)(x-2)>0
綜上:當(dāng)1<x<2時(shí),(x-1)(x-2)<0
當(dāng)x<1或x>2時(shí),(x-1)(x-2)>0
(1)填寫(xiě)下表:(用“+”或“-”填入空格處)
(2)由上表可知,當(dāng)x滿足
時(shí),(x+2)(x+1)(x-3)(x-4)<0;
(3)運(yùn)用你發(fā)現(xiàn)的規(guī)律,直接寫(xiě)出當(dāng)x滿足
時(shí),(x-7)(x+8)(x-9)<0.
|
x<-2 |
-2<x<-1 |
-1<x<3 |
3<x<4 |
x>4 |
x+2 |
- |
+ |
+ |
+ |
+ |
x+1 |
- |
- |
+ |
+ |
+ |
x-3 |
- |
- |
- |
+ |
+ |
x-4 |
- |
- |
- |
- |
+ |
(x+2)(x+1)(x-3)(x-4) |
+ |
- |
|
|
|