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#1 2009-12-15 12:45:32

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Fundamental Theorem of Algebra

After several drafts, herewith I present: The Fundamental Theorem of Algebra

Comments, corrections, etc please smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2009-12-15 13:30:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Fundamental Theorem of Algebra

Hi MathsisFun;

No errors that I found. Looks good. Keep it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2009-12-15 14:47:20

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,582

Re: Fundamental Theorem of Algebra

Wow!  That's excellent!  I'll have to take a look around this site, it is really getting amazing.
I used the hex/binary/decimal converter the other day, found it from google or bing.


igloo myrtilles fourmis

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#4 2009-12-15 16:19:12

careless25
Real Member
Registered: 2008-07-24
Posts: 555

Re: Fundamental Theorem of Algebra

Nicely done!

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#5 2009-12-16 06:58:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Fundamental Theorem of Algebra

Good page!
One thing I'd change is where you talk about multiplicity. You use the example x^4 + x^3 = 0, say that it has two distinct roots, and include a graph to help illustrate.

The problem is that the roots aren't clearly visible from the graph. I'd either zoom in closer to the x-axis, or choose a different example that graphs more nicely.


Why did the vector cross the road?
It wanted to be normal.

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#6 2009-12-16 09:30:09

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Fundamental Theorem of Algebra

Thanks guys!

mathsyperson wrote:

... I'd either zoom in closer to the x-axis, or choose a different example that graphs more nicely.

Good point, will work on it smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2009-12-16 09:36:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Fundamental Theorem of Algebra

Hi MathsisFun;

I know you are trying to show multiplicity but maybe using a lower order equation to do it might be better. The higher the order of the poly the flatter will be the graph on either side of the root. This will make it difficult to see.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#8 2009-12-16 12:48:10

ccmint
Member
Registered: 2009-10-11
Posts: 22

Re: Fundamental Theorem of Algebra

Great job! For the multiplicity section I would suggest adding that if the multiplicity of a factor is even then the graph will be tangent with the x-axis at those roots and if odd the graph will cross the x-axis at those roots. up

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#9 2009-12-17 02:33:09

ccmint
Member
Registered: 2009-10-11
Posts: 22

Re: Fundamental Theorem of Algebra

"A "root" (or "zero") is where the function crosses the x-axis "

Maybe this should be reworded to 'A "root" (or "zero") is a value where the function equals 0' because the function doesn't have to cross the x-axis, but it could be tangent with it. And then show a example: f(3) = 3^2 + 4(3) - 21 = 0

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#10 2009-12-17 10:54:35

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: Fundamental Theorem of Algebra

Why not keep it simple and clear?

You might aswell do it right.

Also, thought about proving the following, or is it out of your scope?

Last edited by Patrick (2009-12-17 11:00:05)


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#11 2009-12-17 11:49:50

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

Re: Fundamental Theorem of Algebra

Thanks for the suggestions.

I have updated the page now smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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