1. When 6x^3-13x^2+px-5 is divided by 3x^2-qx+1 , the quotient and the remained are 2x-1 and 3x+r respectively . Find the values of p ,q ,r .
2. When 6x^3-19x^2+ax+b is divided by 3x^2-11x-4 , the remainder is 3x-2 . Find the values of a and b .
F.4 more about polynomails
2011-03-26 4:24 pm
回答 (1)
2011-03-26 5:47 pm
✔ 最佳答案
1)6x³ - 13x² + px - 5 = (3x² - qx + 1)(2x - 1) + 3x + rPutting x = 0 :- 5 = - 1 + r
r = - 46x³ - 13x² + px - 5 = (3x² - qx + 1)(2x - 1) + 3x - 4Putting x = 1/2 :
6/8 - 13/4 + p/2 - 5 = 3/2 - 4
3 - 13 + 2p - 20 = 6 - 16
p = 106x³ - 13x² + 10x - 5 = (3x² - qx + 1)(2x - 1) + 3x - 4Putting x = 1 :
6 - 13 + 10 - 5 = (3 - q + 1)(2 - 1) + 3 - 4
- 2 = (4 - q) - 1
q = 5
2)6x³ - 19x² + ax + b = Q(x) * (3x² - 11x - 4) + 3x - 26x³ - 19x² + ax + b = Q(x) * (3x + 1)(x - 4) + 3x - 26x³ - 19x² + (a-3)x + b+2 = Q(x) * (3x + 1)(x - 4)Putting x = 4 :384 - 304 + 4a-12 + b+2 = 0
4a + b + 70 = 0 .....(1)Putting x = - 1/3 :- 6/27 - 19/9 + (3-a)/3 + b+2 = 0
- 2 - 19 + 9-3a + 9b+18 = 0
9b - 3a + 6 = 0 .....(2)(1)*9 - (2) :36a + 3a + 630 - 6 = 0a = - 16b = - 6
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