In each of the following , find the value(s) of k .
1 . When x²-4x-3 is divided by x+k , the reminder is -6 .
2 . When 4x²-2x+1 is divided by 2x+k , the reminder is 3k .
3 . Let f(x) = x³-px²+2x+q . When f(x) is divided by x-2 and x-3 , the reminders are -5 and -4 respectively . Find the values of p and q .
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2008-11-17 10:00 am
回答 (1)
2008-11-17 7:15 pm
✔ 最佳答案
1.Put x = -k.
k^2 + 4k - 3 = -6
k^2 + 4k + 3 = 0
(k +1)(k+3) = 0
k = -1 or -3.
2.
Put x = -k/2
k^2 +k + 1 = 3k
k^2 - 2k + 1 = 0
(k -1)^2 = 0
k = 1.
3.
Put x = 2
8 - 4p + 4 + q = -5
-4p + q = -17................(1)
Put x = 3.
27 - 9p + 6 + q = -4
-9p + q -37.....................(2)
(1) - (2) we get
5p = 20
p = 4.
so q = -17 + 16 = -1 from (1).
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