a-maths~~~~~~~~~~~~~~

上面的b)部出錯了~~~
a) 兩根積 = - 1 / 12
所以兩根必是符號相反的實數[ 1個正數乘1個負數才出負數]。
b) 設兩根為3a和-4a。
3a- 4a = - k / 12
a = k / 12 --- ( 1 )
3a ( - 4a ) = - 1 / 12
a^2 = 1 / 144
a = 1 / 12 或 - 1 / 12 --- ( 2 ) [開方有正負的]
代( 2 )入( 1 ),
1 / 12 = k / 12 或 - 1 / 12 = k / 12
k = 1 或 -1



2007-10-10 13:35:12 補充：
設兩根為a,-4a/3都是可以的, 其實只要符合兩根之比為3:-4這個條件便可以了, 即是:a:(-4a/3) = 3:-43a:-4a = 3:-4

2007-10-10 13:37:24 補充：
再補充一點: 3a- 4a = - k / 12 是根據兩根和而得出, 3a ( - 4a ) = - 1 / 12是根據兩根積而得出。

a) 兩根乘埋 = c/a = -1/12
1正乘1負=負數, 兩根必是符號相反的實數.

b) 假設1根=y, 2根= (-4/3)y --> 因為兩根之比為3:-4
所以兩根乘埋:
y(-4/3)y = -1/12
(-4/3)y^2 = -1/12
y^2 = 1/16
y = +- 1/4 ------- (1) --> 開方出正負+-數

將(1)代入方程: 12(+-1/4)² + k(+-1/4) -1 = 0 --> 因為y是方程的根
3/4 + k(+-1/4) = 1
k(+-1/4) = 1-3/4
k(+-1/4) = 1/4
k = 1 or k = -1

a)
let a and b be the two root,
produvt of root=ab=-1/12
the product of 2 number is negative,
so one must positive and one must negative
b)
let 3x be a root, and -4x be another root,
product of root
3x(-4x)=-1/12
x=1
sum of root
3x-4x=-k/12
-1=-k/12
k=12