When a certain polynomial f(x) is divided by (x-1)(3x+2), the remainder is
px+q. When f(x) is divided by x-1, the remainder is -4; when f(x) is divided by 3x+2,the remainder is 6.Find the values of p and q.
F.4 maths
2008-05-01 11:27 pm
回答 (1)
2008-05-01 11:37 pm
✔ 最佳答案
Let f(x) = (x - 1)(3x +2)Q(x) + (px + q) By remainder theorem, f(1)= -4
i.e. (1 - 1)[3(1) + 2]Q(1)+ (p + q) = -4
p + q = -4 ─── (1)
By remainder theorem,f(-2/3) = 6
i.e. [1 – (-2/3)][3(-2/3)+ 2]Q(-2/3) + [p(-2/3) + q] = 6
-2p + 3q = 18 ───(2)
(1) X 2 + (2):
5q = 10
q = 2
p = -6
參考: Myself~~~
收錄日期: 2021-04-13 18:45:41
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