(1)求以下各題中的商和餘式。
(a) x^3 + 4x - 6 除以 x-2
(b) 5x^3 + 7x^2 - 8x +1 除以 x^2+3
(2) 若(x-5)為(x^2-7x+c)的因子，求ｃ的值。
(3)若(a-2)和(a+3)均為 a^3 - pa^2 - qa - 6的因子，求p和q。
(4)(a)証明(x-3)是(x^3+2x^2-9x-18)的因子。
(b)由此，解方程 x^3+2x^2 - 9x -18 =0
PLZZ/\/\"
2007-08-13 12:58 am
回答 (2)
2007-08-13 2:32 am
✔ 最佳答案
1a)x^3 + 4x - 6 = (x-2)(x^2 + 2x + 8) + 10
b)
5x^3 + 7x^2 - 8x +1 = (x^2+3)(5x+7) + (-23x - 20)
用長除法,呢度唔識打比你睇,只比答案你
2)
設 f(x) = x^2-7x+c
f(5) = 25 - 35 + c = 0 (因子既性質)
c = 10
3)
設 f(a) = a^3 - pa^2 - qa - 6
f(2) = 8 - 4p - 2q - 6 = 0
2p - q = 1 -------------------- (1)
f(-3) = -27 - 9p + 3q - 6 = 0
3p - q = -11 ---------------- (2)
(2) - (1), p = -12
q = -25
4)
設 f(x) = x^3+2x^2-9x-18
f(3) = 27 + 18 - 27 - 18 = 0
所以 (x-3)是(x^3+2x^2-9x-18)的因子
b)
用長除法,
x^3+2x^2-9x-18 = (x-3)(x^2+5x+6)
= (x-3)(x+3)(x+2) (二次方程,好易分解)
2007-08-22 7:57 am
話我運吉?
10 個負評你應得!
10 個負評你應得!
收錄日期: 2021-04-23 20:01:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070812000051KK03197