Math Is Fun Forum

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.

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)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Polynomial Ecuation

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Polynomial Ecuation

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Polynomial Ecuation

hi Yusuke00

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

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Polynomial Ecuation

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Polynomial Ecuation

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

So what does R[X] mean ?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Polynomial Ecuation

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