f4 polynomials

2010-02-01 5:07 am
if 3x^3+7x^2-(5k+2)x-2k is divisivle by 3x+1 find the value of k

回答 (1)

2010-02-01 5:23 am
✔ 最佳答案
3x^3+7x^2-(5k+2)x-2k is divisible by 3x+1 = 3(x + 1/3)
So 3x^3+7x^2-(5k+2)x-2k is divisible by (x + 1/3),
By remainder theorem :
3(-1/3)^3 + 7(-1/3)^2 - (5k+2)(-1/3) - 2k = 0
-1/9 + 7/9 + (5/3)k + 2/3 - 2k = 0
-k/3 = - 4/3
k = 4


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