數學急要...

數學(二次方程)
若下列的二次方程有2個不相等的實根,求k值的範圍。
1)
X2+3X-K-1=0
判別式大於零
B2 – 4AC > 0
32 – 4(1)(-K-1) > 0
32 +4K + 4 > 0
4K > - 13
K > -13/4

若下列的二次方程沒有實根,求k值的範圍。
2)
(k+1)X2=4X-1
(k+1)X2-4X+1=0
B2 – 4AC < 0
(-4)2 – 4(k-1)(1) < 0
16 – 4k + 4 < 0
-4k < -20
k > 5

3)
3X(X-2)=3X-k
3X2 – 6X – 3X + K = 0
3X2 – 9X + K = 0
B2 – 4AC < 0
(-9)2 – 4(3)(K) < 0
81 – 12K < 0
-12K < - 81
K > 6.75

若下列的二次方程有實根,求k值的範圍。
4)
X2+3X+5k-9=0
B2 – 4AC > 0
(3)2 – 4(1)(5k-9) > 0
9 – 20k + 36 > 0
-20k > -45
k < 9/4

5)
k(2X+1)=2-kX2
kx2 + 2kx + k – 2 = 0
B2 – 4AC > 0
(2k)2 – 4(k)(k-2) > 0
4k2 – 4k2 + 9 >0
k 可以是任何數

(1)
X^2+3X-K-1=0
如有2個不相等的實根, 3^2 - 4(1)(-k-1) larger than 0

3^2 - 4(1)(-k-1) larger than 0 ----- 因為呢度display唔到大過/ 細過符號, 所以用文字代替
9 + 4K + 4 larger than 0
4K larger than -13
K larger than -13/4

(2)
(k+1)X^2=4X-1
(k+1)X^2 - 4X + 1 = 0
如沒有實根, (-4)^2 - 4(k+1)(1) smaller than 0

(-4)^2 - 4(k+1)(1) smaller than 0
16 - 4K-4 smaller than 0
12 smaller than 4K
3 smaller than K, i.e.
K larger than 3

(3)
3X(X-2)=3X-k
3X^2 - 6X = 3X - k
3X^2 - 9X + k = 0
如沒有實根, (-9)^2 - 4(3)(k) smaller than 0

(-9)^2 - 4(3)(k) smaller than 0
81 - 12k smaller than 0
21 smaller than 12k
21/12 smaller than k
i.e. k larger than 21/12

(4)
X^2+3X+5k-9=0
如有實根, (3)^2 - 4(1)(5k-9) larger than or = 0
(3)^2 - 4(1)(5k-9) larger than or = 0
9 - 20k + 36 larger than or = 0
45 larger than or = 20k
9/4 larger than or = k
i.e. K smaller than or = 9/4

(5)
k(2X+1)=2-kX^2
2kX + k -2 + kX^2 = 0
kX^2 + 2kX + (k-2) = 0

如有實根, (2k)^2 - 4(k)(k-2) larger than or = 0
(2k)^2 - 4(k)(k-2) larger than or = 0
4k^2 - 4k^2 + 8k larger than or = 0
8k larger than or = 0
k larger than or = 0

你識&quot;D&quot;吧??
equation=ax^2+bx+c
D=b^2-4ac
有2個不相等的實根,D&gt;0
沒有實根,D&lt;0
有一個實根,D=0
有實根(可以係得一個or2個),D&gt;=0
1)D=3^2-4(1)(-k-1)
= 9+4k+4
=13+4k&gt;0
so,k&gt;-13/4

2)(k+1)x^2-4x+1=0
D=(-4)^2-4(k+1)(1)
=16-4k-4
=12-4k&lt;0
so,k&gt;3

3)3x^2-6x=3x-k
3x^2-9x+k=0
D=(-9)^2-4(3)(k)
=81-12k&lt;0
so,k&gt;27/4

4)D=3^2-4(1)(5k-9)
=9-20k+36
=45-20k&gt;=0
so,k&lt;=9/4

5)2kx+k=2-kx^2
kx^2+2kx+k-2=0
D=(2k)^2-4(k)(k-2)
=4k^2-4k^2+8k
=8k&gt;=0
so,k&gt;=0
明唔明??要睇清楚,d&lt;,&gt;,&gt;=,呢d符號ge用法.
1)-x&gt;1
x&lt;-1
2) x-1&gt;0
x&gt;1
3)-x&lt;1
x&gt;-1
4)x+4&gt;0
x&gt;-4
注意正負符號!!
&gt;= or &lt;=都係同樣做法

2006-10-18 18:55:39 補充：
你識D吧??有2個不相等的實根,D大過0沒有實根,D細過0有一個實根,D=0有實根(可以係得一個or2個),D大=01)13 4k大0so,k大-13/42)2-4k大0so,k細33)81-12k細0so,k大27/44)45-20k大=0so,k細=9/45)8k大=0so,k大=0明唔明??要睇清楚大,細,大=,呢d符號ge用法.1)-x大1x細-12) x-1大0x大13)-x細1x大14)x 1細0x細1注意正負符號!!大= or 細=都係同樣做法