中4 maths (要步驟)

(2)(a) L1: x + 3y – 5 = 0
L1斜率為 -1/3
L2 // L1所以L2斜率也為 -1/3
L2方程 (y – 3)/(x + 2) = -1/3
3(y – 3) = -(x + 2)
x + 3y – 7 = 0
(b) 代 (-5,4)入L2方程
-5 + 12 – 7 = 0等式成立,所以(-5,4)在L2上

2010-01-07 20:30:35 補充：
(4) 4(x^2 – 3x) + k – 3 = 0沒有實根
4x^2 – 12x + (k-3) = 0沒有實根
判別式 12^2 – (4)(4)(k-3) < 0
144 – 16(k-3) < 0
9 < k – 3
12 < k

2010-01-07 20:32:28 補充：
(9) f(x) = Ax^3 + 2x^2 + Bx + 2
f(-2) = -8A + 8 – 2B + 2 = 0
-4A + 5 – B = 0 … (1)
f(-1) = -A + 2 – B + 2 = 8
-A – 4 – B = 0 …(2)
(2) – (1) => 3A – 9 = 0 => A = 3
代入(1), -12 + 5 – B = 0 => B = -7
f(x) = (x+2)(3x-1)(x-1)

2010-01-09 00:54:59 補充：
(1) 3x^2 – 8x + 2 = 0
(a) 兩根之和α + β = 8/3
兩根之積αβ = 2/3
(b) 以1/α及1/β為根的二次方程
兩根之和1/α + 1/β = (α+β)/(αβ) = (8/3)/(2/3) = 4
兩根之積(1/α)(1/β) = 1/(αβ) = 3/2
二次方程為 x^2 – 4x + 3/2 = 0 或2x^2 – 8x + 3 = 0
(2)(a) L1: x + 3y – 5 = 0
L1斜率為 -1/3
L2 // L1所以L2斜率也為 -1/3
L2方程 (y – 3)/(x + 2) = -1/3
3(y – 3) = -(x + 2)
x + 3y – 7 = 0
(b) 代 (-5,4)入L2方程
-5 + 12 – 7 = 0等式成立,所以(-5,4)在L2上
(3) (2x-1)(x+1) = (x+1)
(2x – 1)(x + 1) – (x + 1) = 0
(2x – 2)(x + 1) = 0
2x – 2 = 0 或x + 1 = 0
x = 1或 x = -1
(4) 4(x^2 – 3x) + k – 3 = 0沒有實根
4x^2 – 12x + (k-3) = 0沒有實根
判別式 12^2 – (4)(4)(k-3) < 0
144 – 16(k-3) < 0
9 < k – 3
12 < k
(5) f(x) = x^2 + 5x – 3
f(k) = k^2 + 5k – 3 = 3k
k^2 + 2k – 3 = 0
(k + 3)(k – 1) = 0
k = -3或 k = 1
(6) f(x) = ax/(x – b)
f(1) = a/(1 – b) = 2 … (1)
f(3) = 3a/(3 – b) = 5 … (2)
(2)/(1) => 3(1 – b)/(3 – b) = 5/2
6(1 – b) = 5(3 – b)
6 – 6b = 15 – 5b
-9 = b
代入(1), a/(1 + 9) = 2 => a = 20
(7) (-5x^3 + 3x^2 – 2) / (x^2 – 3)
以長除計算商式為-5x+3餘式為-15x+7

圖片參考：http://img503.imageshack.us/img503/5360/div1.png



(8) 設f(x) = x^2009 – 3x + 4
f(x) 除以x+1的餘數 = f(-1) = (-1)^2009 – 3(-1) + 4 = -1 + 3 + 4 = 6
因當x=7時f(x) = 7^2009 – 21 + 4 = 7^2009 – 17及 x+1 = 8
所以7^2009 – 17除以8的餘數為6
(9) f(x) = Ax^3 + 2x^2 + Bx + 2
f(-2) = -8A + 8 – 2B + 2 = 0
-4A + 5 – B = 0 … (1)
f(-1) = -A + 2 – B + 2 = 8
-A – 4 – B = 0 …(2)
(2) – (1) => 3A – 9 = 0 => A = 3
代入(1), -12 + 5 – B = 0 => B = -7
(b) f(x) = 3x^3 + 2x^2 – 7x + 2 其一因式為x + 2
f(x) / (x + 2)

圖片參考：http://img503.imageshack.us/img503/1199/div2.png



= 3x^2 – 4x + 1 = (3x – 1)(x – 1)
故此f(x) = (x+2)(3x-1)(x-1)

good............

做完= =~~是但啦~幫到人米得囉~~~= =不過唔知correct or not = =

2010-01-07 21:38:35 補充：
我錯好多~Sorry,
最近心情唔係太好~~唔可以太集中精神~~Sorry ><"

你睇睇你打左D咩出黎?

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