急 ! F6數1題 #11.

Bid

2014-03-03 1:43 am

請詳細步驟教我計下條 : When f(x) is divided by 2x+1, the remainderis 1. When f(x) is divided by 2x-1, the remainder is 5. (a) Find the remainder when f(x) isdivided by 4x^2-1.(b) Find the remainder when[f(x)-3x-2]^2 is divided by 2x-1. Is it divisible by 2x-1 ?

回答 (1)

用戶4366

2014-03-03 2:33 am

✔ 最佳答案

f(x) = (2x+1)(2x-1)Q"(x) + ax+b

f(-1/2) = [2(-1/2)+1][2(-1/2)-1]Q"(x) + (-1/2)a+b = 1
-a+2b=2 ..... (1)

f(1/2) = [2(1/2)+1][2(1/2)-1]Q"(x) + (1/2)a+b = 5
a+2b = 10 ... (2)

Solve (1) and (2) gives a = 4 and b = 3

f(x) = (2x+1)(2x-1)Q"(x) + 4x + 3

g(x) = [f(x) - 3x - 2]²

g(x) = [ (2x+1)(2x-1)Q"(x) + 4x + 3 - 3x - 2 ]²

g(x) = [ (2x+1)(2x-1)Q"(x) + x + 1 ]²

g(1/2) = [ 2(1/2)+1][2(1/2)-1)Q"(x) + (1/2) + 1 ]
=[(1/2)+1]²
=9/4

2014-03-02 18:36:22 補充：
g(x) = [ (2x+1)(2x-1)Q"(x) + x + 1 ]²

g(1/2) = [ 2(1/2)+1][2(1/2)-1)Q"(x) + (1/2) + 1 ]²　　　　打漏了 2 次方
=[(1/2)+1]²
=9/4

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