急 F5 Inequalities Unknown2C01

簡單點二次不等式的解要看他的不等號.
(x-3)(x+4)≦0 解-4≦x≦3, 因為只有x>-4且x<3這二次式才會小於0,而當x=3or-4時都等於0.
因為很簡單只要記主依4句!
當a>0且α>β時,
a(x-α)(x-β)>0,解為x<β or x>α
a(x-α)(x-β)≧0,解為x≦β or x≧α
a(x-α)(x-β)<0,解為β<x<α
a(x-α)(x-β)≦0,解為β≦x≦α

2012-08-17 14:03:34 補充：
2.
(x-2)(3x+1)>0
(x-2)3(x+1/3)>0
3(x-2)(x+1/3)>0 上面第1條.
3(x-2)[x-(-1/3)]>0 x<-1/3 or x>2 重一定記得α>β,在其解α=2,β=-1/3

2012-08-17 14:09:08 補充：
3.
2x(x-5)≧0
2x^2-10x≧0
在依題不是上面的式形, 那麼就要教導出上式前,要知的知識,
對於ax^2+bx+c的不等式ab>0則a同b同號,即是a>0且b>0 或者a<0且b<0
如ab<0,則a同b不同號,即a>0且b<0或a<0且b>0 .
2x^2-10x a=2 ,b=-10 ,ab=-20 則ab<0 ,即a>0且b<0 或 a<0且b>0
2x^2-10x≧0其實好像和上面式不同,其實是相同的,
2x(x-5)≧0
2(x-0)(x-5)≧0 記得α>β α=5 ,β=0 x≦0 or x≧5

2012-08-17 14:14:30 補充：
x^2<16 移項
x^2-16<16-16
x^2-16<0
x^2-4^2<0
(x-4)(x+4)<0
(x-4)[x-(-4)]<0 上式第三條a(x-α)(x-β)<0,解為β<α
在這式a=1,α=4,β=-4,因此β<α⇒-4<4

a*x^2 + b*x + c
"a" = positive (+) then curve looks like "happy face"
"a" = negative (-) then curve looks like "sad face"
Drawing the curve on paper: (case of a=+)
If "=>" use "hand" cover the bottom portion of the curve below "x-axis", you will know why the answer is "OR"
If "=<" use "hand" cover the top portion of the curve above "x-axis", you will find out why the answer is "AND".

YOU DO YOURSELF FOR THE CASE OF "a=-"

Btw, the answer 1) -4<=x,=3