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標題: Polynomial(追加一個問題-o-) [打印本頁]

作者: AYuMe 時間: 08-10-10 07:51 PM 標題: Polynomial(追加一個問題-o-)

1. Let f(x) be a polynomial with real coefficients
It is given that the leading coefficient of f(x) is 2 and deg f(x) = 4
When f(x) is divided by (x + 2) , the remainder is -28
When f(x) is divided by (x^2 - 1) , the remainder is (13x + 1)
Let r(x) be the remainder when f(x) is divided by (x + 2)(x^2 - 1)

(a)Find r(x)

(b)If f(x) is divisible by (x - 2) , find f(x)
原來還有(b)..

[ 本帖最後由 AYuMe 於 2008-10-11 10:34 AM 編輯 ]

作者: 9546312 時間: 08-10-10 09:01 PM

Let
f(x)=(x + 2)Q(x)-28
f(x)=(x^2 - 1)T(x)+(13x + 1)
Let f(x)=(x + 2)(x^2 - 1)E(x)+(Ax^2+Bx+C)
f(-2)=-28
f(1)=14
f(-1)=-12
so....
R(-2)=-28
R(1)=14
R(-1)=-12
solve A,B,C....R(x)=Ax^2+Bx+C
好似唔岩...用唔到你個leading coefficient.....又唔知點delete...等其他人答你好過....

[ 本帖最後由 9546312 於 2008-10-10 09:04 PM 編輯 ]

作者: AYuMe 時間: 08-10-10 09:13 PM

會唔會那個數據是多餘的=]?

作者: AYuMe 時間: 08-10-11 02:55 PM

請問 x^3 - 5x +6(2)^1/2 既root係咩野?

作者: ^^jimmy^^ 時間: 09-6-7 03:08 PM

Since the leading coefficient of f(x) is 2 and deg f(x) = 4
Hence, let E(x) = 2x + D [f(x)=(x + 2)(x^2 - 1)E(x)+(Ax^2+Bx+C)]
Then, put x = 2 into f(x) (f(2) = 0)... solve D...
唔知岩唔岩-.-"

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