F.4 mathematics

2012-04-11 10:44 pm
已知當ax^(2)+bx-7除以x-3時,所得的餘數是14;當2x^(2)+ax+b除以x+3時,所得的餘數是1.求a和b的值

回答 (2)

2012-04-11 11:15 pm
✔ 最佳答案
代 x = 3:

9a + 3b - 7 = 14

9a + 3b = 21 ... (1)

代 x = -3:

18 - 3a + b = 1

3a - b = 17 ... (2)

得 a = 4, b = -5
參考: 原創答案
2012-04-11 11:19 pm
Let q be the quotient:

ax^2+bx-7=(x-3)q+14
代3入x9a+3b-7=14
9a+3b=21
3a+b=7-----(1)
----------------------------
2x^2+ax+b=(x+3)q+1
代-3入x
18-3a+b=1
3a-b=17(2)
----------------------
(1)+(2):6a=24
a=4//
3a+b=7
12+b=7
b= -5//


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