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#1
Nov 24 2014 01:25pm
n=3 (degree)
zeros= -1, -2+3i are given. -2-3i is paired.

Can anyone give me tips on how to solve? I keep messing up somewhere or there is no correct answer, which is a possibility.
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#2
Nov 24 2014 01:48pm
You work backwards, the zeros of the function are given to you thus you work backwards by multiplying the zeros out.


Ie: given degree of polynomial 2 and zeros of -2,3 we can find polynomial by multiplying out (x+2)(x-3)=x^2-x-6

Here is work hopefully you fully understand.


This post was edited by Xx Shin3d0wn xX on Nov 24 2014 02:12pm
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#3
Nov 24 2014 02:12pm
If a1, a2, a3, ... a_n are the n complex roots of a polynomial P, then :

P(X) = k.( X - a1 ).( X - a2 ).( X - a3 )...( X - a_n )

for some complex number k.
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#4
Nov 24 2014 02:35pm
Quote (Xx Shin3d0wn xX @ Nov 24 2014 01:48pm)
You work backwards, the zeros of the function are given to you thus you work backwards by multiplying the zeros out.


Ie: given degree of polynomial 2 and zeros of -2,3 we can find polynomial by multiplying out (x+2)(x-3)=x^2-x-6

Here is work hopefully you fully understand.
http://s29.postimg.org/env2exwx3/image.jpg


Thanks! Nice to know I did it correctly. The answer choices were:
a.) f(x) = x^3 + 3x^2 + 15x - 13
b.) f(x) = x^3 + 3x^2 + 9x - 13
c.) f(x) = x^3 - 4x^2 +9x - 13
d.) f(x) = x^3 +5x^2 +9x - 14
e.) No correct Answer

So it's probably (e)

This post was edited by Iffy00 on Nov 24 2014 02:35pm
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#5
Nov 24 2014 02:51pm
Did you post correct zeros? Given those solutions b is correct if x=1,-2+3i,-2-3i
But given the roots x=-1,-2-3i,-2+3i the correct poly is one given by me and therefore e would be the solution
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#6
Nov 24 2014 03:49pm
Quote (Xx Shin3d0wn xX @ Nov 24 2014 02:51pm)
Did you post correct zeros? Given those solutions b is correct if x=1,-2+3i,-2-3i
But given the roots x=-1,-2-3i,-2+3i the correct poly is one given by me and therefore e would be the solution


Yes,

N=3
Zeros = -1, -2+3i

Are given, Find Nth Polynomial Function.

You had the same answer as me, I was just making sure I wasn't doing it wrong. I really appreciate your help!
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#7
Nov 24 2014 05:22pm
Quote (Iffy00 @ Nov 24 2014 04:49pm)
Yes,

N=3
Zeros = -1, -2+3i

Are given, Find Nth Polynomial Function.

You had the same answer as me, I was just making sure I wasn't doing it wrong. I really appreciate your help!



No problem ask anytime you need help, I love doing math on the side (sounds weird but it's something I enjoy) bc this is what my undergrad degree is in and what I studied in graduate school for a bit.
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#8
Nov 24 2014 11:02pm
Quote (Xx Shin3d0wn xX @ Nov 24 2014 02:48pm)
You work backwards, the zeros of the function are given to you thus you work backwards by multiplying the zeros out.


Ie: given degree of polynomial 2 and zeros of -2,3 we can find polynomial by multiplying out (x+2)(x-3)=x^2-x-6

Here is work hopefully you fully understand.
http://s29.postimg.org/env2exwx3/image.jpg


omg I'm so happy I'm a pilot... fuck that.
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