polynomials 問題

[匿名]

2010-02-12 7:35 pm

1) If f (x) = x^3 - 2kx^2 - 27 is divisible by x-k, find the value of k

2)it is given that x-1 is a factor of f(x) = 2x^3 + 2x^2 + kx +6

a ) find the value of k

b) Hence factorixe f(x)

3)when f(x) = 2x^3 + px^2 +7x + q is divided by x and x-1 the remainders are
both 6

a) find the value of p and q

b) solve the equaton f(x) = 6

4)when a polynomial f(x) is divided by x - 1 and x -2 the remainders are 0 and -4 respectively .find the remainder when f(x) is divided by (x-1) (x-2)

5)Use the division algorithm to find the remainder when 2x^3+5 x - 8 is divided by

五明占做請高手幫忙有五占
x(x + 1).

回答 (1)

用戶7639

2010-02-12 10:48 pm

✔ 最佳答案

1) f(k)=0
k3-2k(k)2-27=0
k3-2k3-27=0
k3=27
k=3

2a)f(1)=0
2(1)3+2(1)2+k(1) +6=0
2+2+k+6=0
k=-10

b)f(x)= 2x3+2x2-10x+6
=(x-1)2(x+3)

3a)f(0)=6
2(0)3+p(0)2+7(0)+q=6
q=6

f(1)=6
2(1)3+ p(1)2+7(1)+q=6
2+p+7+q=6
p=-q-3
p=3

b) f(x)=6
2x3-3x2+7x+6=6
2x3-3x2+7x=0
x(2x2-x+7)
x=0

4) f(x)=(x-1)Q1(x)
f(x)=(x-2)Q2(x)-4
Let f(x)=(x-1)(x-2)Q(x)+k(x-1)
f(2)=-4
k=-4
∴the remainder is -4x+4.

2010-02-13 10:42:26 補充：
第5題:
http://i.imagehost.org/0671/Crazy002.jpg

參考: , 第5題 by 張遼

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