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#1 2014-02-09 04:41:46

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Question about polynomial ecuation

Hey guys.I have a little question or just a personal wonder about them.


Question is:
for any
?
What about 
?
Test:

Last edited by Yusuke00 (2014-02-09 04:57:39)

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#2 2014-02-09 04:42:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,786

Re: Question about polynomial ecuation

Hi;

Please adjust the latex.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-02-09 04:52:09

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

Done yeah cool now i found out how it works. hehe

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#4 2014-02-09 04:53:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,786

Re: Question about polynomial ecuation

Hi;

How can K be an element of R?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2014-02-09 04:55:51

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

It's N* sorry math. I don't really know how to write N* or R*+.How you do that?

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#6 2014-02-09 04:58:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,786

Re: Question about polynomial ecuation

You can just put N or R. You can use

http://www.codecogs.com/latex/eqneditor.php

for all ypur latexing.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2014-02-09 09:46:33

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

Not any opinions/ideas yet?

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#8 2014-02-09 18:01:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Question about polynomial ecuation

Yusuke00 wrote:

Hey guys.I have a little question or just a personal wonder about them.


Question is: Is
for any
?
What about 
?

Fixed the post a bit.

Why would you think they cannot be positive?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2014-02-10 02:35:06

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

You got it wrong.
In my opinion the first one is always positive for any x real but i don't really know how to prove it.

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#10 2014-02-10 02:47:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,786

Re: Question about polynomial ecuation

Hi;

That is the gf for that sum. It is obviously positive when x >=0. You might now try to prove that the numerator and denominator have the same sign for x<0.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2014-02-10 03:19:38

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

That would be quite hard.
I know the problem is to prove that x does not have roots on (-1,0) because it's easy to see on the other cases.Ideas?

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#12 2014-02-10 03:35:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,786

Re: Question about polynomial ecuation

Hi;

Is it really that hard?

Take the numerator when x<0. It is obvious that x^(2k+1) is always negative and therefore x^(2k)-1 is always negative.

Now the denominator is obviously negative for x<0, so we have (-) / (-) which is always positive.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#13 2014-02-10 04:02:37

Yusuke00
Member
Registered: 2013-11-19
Posts: 43

Re: Question about polynomial ecuation

Indeed,good point you are right.

http://www.mathsisfun.com/data/function-grapher.php?func1=sqrt%28x%29&func2=2

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#14 2014-02-10 15:20:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,532

Re: Question about polynomial ecuation

Or, you could just say that, for any integer n, x^(2n)>0.

Also, I was confused by the question. It seems, by what you wanted, that it should have been "Is f>0 for every x in R?".

Last edited by anonimnystefy (2014-02-10 15:22:08)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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