Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

#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
?
?
Test:

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

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

Re: Question about polynomial ecuation

Hi;

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.

Online

#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

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

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.

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.

Online

#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?

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

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.

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.

Online

#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?

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

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
?
?

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
The knowledge of some things as a function of age is a delta function.

Offline

#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.

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

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.

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.

Online

#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?

Offline

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

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.

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.

Online

#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

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

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
The knowledge of some things as a function of age is a delta function.

Offline