1)if x+1 is a factor of x^3+kx^2-3x+k
2)when the polynomials x^2-2x+1 and 3x^2+x-4are divided by x+p respectively, their remainders are equal.Find the possible values of p.
f.4 a maths
2007-03-22 5:59 am
回答 (2)
2007-03-22 6:07 am
✔ 最佳答案
(1)By factor theorem,
(-1)^3 + k(-1)^2 - 3(-1) + k = 0
-1 + k + 3 + k = 0
2k + 2 = 0
k = -1
(2)
By factor theorem,
(-p)^2 - 2(-p) + 1 = 3(-p)^2 + (-p) - 4
p^2 + 2p + 1 = 3p^2 - p - 4
2p^2 - 3p - 5 = 0
(2p - 5) (p + 1) = 0
p = 5/2 or -1
2007-03-22 6:09 am
1.f(-1)=-1+k+3+k=0
2k=-2
k=-1
2.f(-p)=p^2+2p+1=3p^2-p-4
2p^2-3p-5=0
(2p-5)(p+1)=0
p=5/2 or p=-1
2k=-2
k=-1
2.f(-p)=p^2+2p+1=3p^2-p-4
2p^2-3p-5=0
(2p-5)(p+1)=0
p=5/2 or p=-1
收錄日期: 2021-04-12 18:48:33
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