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#1 2014-02-02 07:28:49

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

Polynomial Ecuation

Hello guys long time no see,got a new exercise:

On R[X] f=X^4-aX^3-aX+1

Proove that if |a|<1 then |x1|=|x2|=|x3|=|x4|=1;
Good luck.

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#2 2014-02-03 07:33:29

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

Re: Polynomial Ecuation

Ok guys a second problem

f(1)=8
f(2)=-5
f(3)=0
f(4)=35

f=?

The thing is i know how to solve the problem but i cannot really solve the system.
f(3)=0 -> x1=3 solution ->f = (X-3)(aX^2+bX+c)==>
==>f=aX^3+(b-3a)X^2+(c-3b)X-3c
so f(3)=0 ==>-3c=0 =>c=0

f(1)=8 ==> a+b=-4
f(2)=-5 ==>-4a-2b=-5==>4a+2b=5
f(4)=35 ==> 16a+4b=35

Can anyone solve the system or at least tell me where i'm wrong ? I'm getting very mad here.

Last edited by Yusuke00 (2014-02-03 09:56:58)

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#3 2014-02-03 08:46:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,729

Re: Polynomial Ecuation

Hi;

f(1)=9
f(2)=-5
f(3)=0
f(4)=35


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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#4 2014-02-03 09:57:39

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

Re: Polynomial Ecuation

bobbym wrote:

Hi;

f(1)=9
f(2)=-5
f(3)=0
f(4)=35

Could you describe your solution step by step please? For f(1)=8 not 9 sorry.

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#5 2014-02-03 14:08:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,729

Re: Polynomial Ecuation

Hi;

After substitution into the general form you get.

Can you solve that or do you need a little more?


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

#6 2014-02-03 19:03:36

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

Re: Polynomial Ecuation

Ok i got those ecuations either.W/E i'm stupid.Thank you.

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#7 2014-02-03 20:31:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,729

Re: Polynomial Ecuation

Are you okay with getting the solutions? if you need help just post back.


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

#8 2014-02-04 02:03:54

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

Re: Polynomial Ecuation

Yes i had the same ecuations,but i've been tired and just couldn't focus yesterday.Got them now thank you.

By the way,any clues on 1st problem?

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#9 2014-02-04 02:08:53

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Polynomial Ecuation

hi Yusuke00

I didn't post earlier because I do not understand what you mean by X1 X2 etc.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2014-02-04 04:33:44

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

Re: Polynomial Ecuation

x1 are the solutions to the ecuation like...
f(x1)=0,f(x2)=0,f(x3)=0,f(x4)=0;
Sorry that's how i know to note them.

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#11 2014-02-04 04:57:52

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Polynomial Ecuation

hi Yusuke00

That's what I thought you meant and that's where my difficulty began.

If you go to this page of the MIF site

http://www.mathsisfun.com/data/function … x)&func2=2

you will find a very useful function grapher.  It even allows you to put in an 'a' and adjust its value using the slider.

This shows no roots at all.

Bob

View Image: yusuke.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2014-02-04 05:19:46

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

Re: Polynomial Ecuation

For a>=1 there are real solutions.For a<1 there are not.That function grapher is for R not for C.

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#13 2014-02-04 05:48:53

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

Re: Polynomial Ecuation

But it's very helpful,i like it.Thank you very much ^_^.

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#14 2014-02-04 06:47:36

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Polynomial Ecuation

On R[X] f=X^4-aX^3-aX+1

So what does R[X] mean ?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#15 2014-02-04 07:53:08

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

Re: Polynomial Ecuation

It means that f(x) =y,y is part of R.

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