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f4 maths4

2008-08-28 9:34 am

1.Let f(x)=x^3+2x^2+k,where k is a contant.If f(-1)=0,find the remainder when f(x) is divided by x-1.
2.If the equation x^2-4x+k=1 has no real roots,then the range of values of k is?
3.If 10^a+b=c,thenb=?

更新1:

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回答 (1)

Uncle Michael

2008-08-28 5:47 pm

✔ 最佳答案

1.
f(x) = x3 + 2x2 + k

f(-1) = 0:

(-1)3 + 2(-1)2 + k = 0

-1 + 2 + k = 0

k = -1

Hence, f(x) = x3 + 2x2 -1

According to the Remainder Theorem, when f(x) is divided by x-1:

Remainder = f(1)
Remainder = (1)3 + 2(1)2 - 1
Remainder = 2

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2.

x2 -4x + k=1

x2 -4x + (k-1) = 0

The above equation has no real roots:

∆ = b2 - 4ac < 0

(-4)2 - 4(1)(k-1) < 0

16 - 4k + 4 < 0

-4k + 20 < 0

4k - 20 > 0

4k > 20

k > 5

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3.
Is 10^a+b represents 10a+b or (10a+b)?

Case 1: 10a+b = c

Case 1: a+b = log(c)

Case 1: b = log(c) -a

Case 2: 10a + b = c

Case 2: b = c - 10a
=

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