When 2x⁴-7x³ -3x² +px+q is divided by(2x² -3x-5),the remainder is 2.
Find p and q
[數學]question about polynomial
2012-03-25 11:02 am
回答 (2)
2012-03-25 11:34 am
參考: 振文
2012-03-25 4:18 pm
2x^2 - 3x - 5 = (2x - 5)(x + 1)
So 2x^4 - 7x^3 - 3x^2 + px + q = (2x - 5)(x + 1)Q(x) + 2
Put x = - 1
2 + 7 - 3 - p + q = 6 - p + q = 2
- p + q = - 4 ..................(1)
Put x = 5/2
625/8 - 875/8 - 75/4 + 5p/2 + q = 2
625 - 875 - 150 + 20p + 8q = 16
20p + 8q = 416
5p + 2q = 104.................(2)
Solving (1) and (2)
p = 16 and q = 12.
2012-03-25 08:20:36 補充：
Note : 0 x Q(x) is always = 0
So 2x^4 - 7x^3 - 3x^2 + px + q = (2x - 5)(x + 1)Q(x) + 2
Put x = - 1
2 + 7 - 3 - p + q = 6 - p + q = 2
- p + q = - 4 ..................(1)
Put x = 5/2
625/8 - 875/8 - 75/4 + 5p/2 + q = 2
625 - 875 - 150 + 20p + 8q = 16
20p + 8q = 416
5p + 2q = 104.................(2)
Solving (1) and (2)
p = 16 and q = 12.
2012-03-25 08:20:36 補充：
Note : 0 x Q(x) is always = 0
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https://hk.answers.yahoo.com/question/index?qid=20120325000051KK00077