F.4 Maths - Ans.fyi 參考答案

F.4 Maths

2010-07-23 3:14 am

1) When the polynomial x^2+4x-3 is divided by x+k, the quotient is x-2.
Find the value of k. (ans=6)

2) If 2x+1 is a factor of 2x^3-x^2+ax-1,find the value of a . (ans= -3)

3) Let f(x) be a polynomial. If f(x) is divisible by x+1,which of the following must be a factor of f(x-2)?
A. x B. x-1 C. x+1 D. x+2 (ans=B)

4)If a straight line l passes through (b,a) and (-a,-b),then the equation of l
is? (ans. y=x+a-b)

5)If (2/4+i)-ki is a real number,where k is a real number,then k=?
(ans= -2/17)

pls show clear steps.thz!

回答 (1)

用戶2053

2010-07-23 5:07 am

✔ 最佳答案

1)x^2+4x-3= (x-2)(x+k) + remainder= x^2 - 2x + kx - 2k + remainder= x^2 + (k-2)x - 2k + remainderSok-2 = 4k = 6

2) By remainder theorem ,2(-1/2)^3 - (-1/2)^2+a(-1/2) -1 = 0- 1/4 - 1/4 - a/2 - 1 = 0a = - 3

3)f(x) is divisible by x+1So f(x-2) is divisible by (x-2) + 1 = x - 1 (B)

4) (y-a)/(x-b) = (a+b)/(b+a)(y-a)/(x-b) = 1y-a = x-by = x + a - b
5) 2/(4+i)-ki = 2(4-i) / [(4+i)(4-i)] - ki= (8 - 2i) / 17 - ki= 8/17 - (2/17)i - ki= 8/17 - (2/17 + k) iSo 2/17 + k = 0 for real .k = -2/17

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