When f(x) is divided by x-k, where k is an integer, the remainder is -2.
Show that k=2.
更新1:
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a question about Pure maths
2009-10-12 1:38 am
Let f(x)=(x-a)(x-b)(x-4)-4, where a and b are integers with a<b<4.
When f(x) is divided by x-k, where k is an integer, the remainder is -2.
Show that k=2.
When f(x) is divided by x-k, where k is an integer, the remainder is -2.
Show that k=2.
回答 (1)
2009-10-12 2:31 am
✔ 最佳答案
By remainder theorem :f(k) = (k-a)(k-b)(k-4)-4 = -2
(k-a)(k-b)(k-4) = 2
Since a and b are integers , k is an integer , so
k-a , k-b , k-4 are integers ;
Since a<b<4 , so k-a > k-b > k-4 .
Only one possible :
k-a = 1 > k-b = - 1 > k-4 = - 2
k = 2 , b = 3 , a = 1
f(x) = (x-1)(x-3)(x-4)-4 divided by x-2
the remainder = f(2) = (2-1)(2-3)(2-4)-4 = - 2 is correct.
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