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November 23, 2014

November 23, 2014

Posted by **Marissa** on Friday, August 17, 2007 at 4:09pm.

B.f(x)= x^2-4x^2+4x-16

C.f(x)= x^2+4x^2+4x+16

D.f(x)= x^2-4x^2-4x+16

2)A.+-1,+-2,+-3,+-6

B.0,+-1,+-2,+-3,+-6,+-1/3,+-2/3

C.+-1,+-2,+-3,+-6,+-1/3,+-2/3

D.+-1,+-3,+-1/6,+-1/3,+-1/2,+-3/2

4)I dont know what they mean either but this is all it says.

A.3x^2-x+5

B.75-30x+3x^2

C.3x^2-15x^2

D.15x^2-3x^3

what do they mean when they say like 2i,what is that?

1)Write a polynomial function of least degree with integral coefficients whose zeros include 4 and 2i.

answer= f(x)= x^2-4x^2+4x-16

2)List all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6

dont know

3)Find all of the rational zeros of f(x)= 4x^3-3x^2-22x-15

dont know

4)Find (f.g)(x) for f(x)= 3x^2 and g(x)= 5-x

answer= 3x^2-15x^2

1. imaginary roots always come in pairs, like in ±2i

so the factors would be (x+2i)(x-2i)(x-4)

expand it and you will have your answer.

2. I tried the factor theorem hoping for some f(a)=0 where a=±1,±2,±3

None worked so I don't know how you are expected to do that one.

You could try ±1/3,±2/3 but that seems a bit too farfetched from the type of questions you seem to have

3. try f(-1) it will be a zero

so x+1 is a factor. Do synthetic division or long division, you should get an answer of 4x^2 - 7x - 15 which factors again.

(see if you can get zeros at x=-1,3,-5/4

4. I don't know if your textbook defines

(f∙g) as f(g(x)) or g(f(x)).

f(g(x)) = f(5-x) = 3(5-x)^2

= 75 - 30x + 3x^2

g(f(x)) = g(3x^2) = 5 - 3x^2

i is the symbol for √(-1), which is the imaginary unit number.

so 2i is really 2√(-1)

in other words i^2 = -1

eg. solve x^2 + 9=0

x^2 = -9

x = ±(√9)(√(-1))

x = ±3√(-1)

x = ±3i

1. After I expanded my answer to #1 above I got x^3 - 4x^2 + 4x - 16 which is the same as B if your first term is x^3, as it should be for all of those answers.

2. for this questions according to the answers I can see that they simply wanted those values that your would try in your f(x) function. As I noted in my first answer, the correct answer would appear to be C

4. So it is B

Look at my first solution how I got that.

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