阅读下列内容后,解答下列各题:几个不等于0的数相乘,积的符号由负因数的个数决定.
例如:考查代数式(x-1)(x-2)的值与0的大小
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,∴(x-1)(x-2)>0
综上:当1<x<2时,(x-1)(x-2)<0
当x<1或x>2时,(x-1)(x-2)>0
(1)填写下表:(用“+”或“-”填入空格处)
(2)由上表可知,当x满足______时,(x+2)(x+1)(x-3)(x-4)<0;
(3)运用你发现的规律,直接写出当x满足______时,(x-7)(x+8)(x-9)<0.
0 156585 156593 156599 156603 156609 156611 156615 156621 156623 156629 156635 156639 156641 156645 156651 156653 156659 156663 156665 156669 156671 156675 156677 156679 156680 156681 156683 156684 156685 156687 156689 156693 156695 156699 156701 156705 156711 156713 156719 156723 156725 156729 156735 156741 156743 156749 156753 156755 156761 156765 156771 156779 366461
例如:考查代数式(x-1)(x-2)的值与0的大小
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,∴(x-1)(x-2)>0
综上:当1<x<2时,(x-1)(x-2)<0
当x<1或x>2时,(x-1)(x-2)>0
(1)填写下表:(用“+”或“-”填入空格处)
(2)由上表可知,当x满足______时,(x+2)(x+1)(x-3)(x-4)<0;
(3)运用你发现的规律,直接写出当x满足______时,(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) | + | - |