maths~~~~~~~

👨🏻‍🏫 學術台數學

用戶7639

2007-10-12 5:36 am

當多項式f(x)除以x-5時,所的的餘數是9:當它除以x+2,所得的餘數是-5。求(x-5)(x+2)時所的餘式。

回答 (1)

Gabriella Montez

2007-10-12 5:47 am

✔ 最佳答案

假設餘式=ax+b:

f ( x ) = ( x - 5 )( x + 2 ) Q ( x ) + ax + b

f (5) = 9

5a + b = 9 --- ( 1 )

f (-2) = -5

-2a + b = -5

b = 2a - 5 --- ( 2 )

代(2)入(1),

5a + 2a - 5 = 9

7a = 14

a = 2

b = 2 ( 2 ) - 5 = -1

所以餘式: 2x-1。

參考: My Maths Knowledge

👍 0 👎 0

收錄日期: 2021-04-23 20:38:25
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071011000051KK03865

檢視 Wayback Machine 備份