(中4數)多項式/除數

2012-07-12 12:09 am
1. 當f(x)除x+1和x-2時,餘式分別是-3/3
求(x+1)(x-2)



2.己知f(x)=5x^3 - 2x^2 + kx -1及 g(x)= -x^3 + 2kx^2 - 3x +4
a) 當f(x)除x-1時,餘數相等,求k

5-2+k-1=-1+2k-3+4
k-8=2k
-8=k

b)由此,求f(x)-g(x)
f(x)-g(x) =5x^3 - 2x^2 -8x -1 +x^3 +16x^2 +3x -4
=6x^3+14x^2 -5x -5
然後就唔識解落去
x我代過正負(1/2/0.5/0.3333333....)都好似唔岩
所以求高手解答.....

3.另外我想搵一個輸入方程毫會show條方程既圖像出黎既website......


感謝....
更新1:

更正 題1係f(X)除(x+1)(x-2)時的餘式!

更新2:

f(x)=(x^2-x+2)Q(x)+ax+b Index of Remainder is smaller than 2 唔好意思 可唔可以比多少少tips 點解ax+b係細過2 ????

回答 (2)

2012-07-12 11:40 pm
✔ 最佳答案
(1)

設當 f(x) 除以 (x + 1)(x - 2) 的商式為 q(x),餘式為 ax + b,則
f(x) = (x + 1)(x - 2)q(x) + ax + b
∵ f(-1) = -3 及 f(2) = 3,則
(-1 + 1)(-1 - 2)q(-1) + a(-1) + b = -3 及 (2 + 1)(2 - 2)q(2) + a(2) + b = 3
a - b = 3 及 2a + b = 3
解聯立方程得 a = 2 及 b = -1
∴ 餘式為 2x - 1

(2)(a)

f(1) = g(1)
5(1)³ - 2(1)² + k(1) - 1 = -(1)³ + 2k(1)² - 3(1) + 4
5 - 2 + k - 1 = -1 + 2k - 3 + 4
2 + k = 2k
k = 2

(2)(b)

f(x) - g(x)
= (5x³ - 2x² + 2x - 1) - (-x³ + 4x² - 3x + 4)
= 6x³ - 6x² + 5x - 5
= (x - 1)(6x² + 5)

(3)

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參考: knowledge
2012-07-12 7:33 am
(x+1)(x-2)=x^2-2x+x-2=x^2-x+2
________
f(x)=(x^2-x+2)Q(x)+ax+b
Index of Remainder is smaller than 2


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