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#1 2013-06-28 05:51:45

romani
Member
Registered: 2013-06-28
Posts: 3

quintic equation and constants

hello! so, I've came accross a problem I can't solve at all :c. The problem is as it follows:

The constant term of

is equal -270, then a=?

I searched how to solve it and found only one solution, but I didn't understand what was done... they turned

into 
and somehow found that k = 2. also, they found "
", which give us a = -3.

That's actually the right answer, but I can't figure out what was done to solve this problem... :c Can you guys explain it to me?

Thanks c:

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#2 2013-06-28 06:05:39

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,531

Re: quintic equation and constants

hi romani

Welcome to the forum.

This involves the binomial theorem.  Do you know this?

Bob


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

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#3 2013-06-28 06:21:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,582

Re: quintic equation and constants

Hi;

Welcome to the forum.

The expansion of that is

from which you see 10a^3  is the constant term.

10 a^3 = - 270

a^3 = - 27

a = -3

Or:

Your latexing did not come out.

That is derived from the binomial theorem. You only have to solve the equation.


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 2013-06-29 03:02:33

romani
Member
Registered: 2013-06-28
Posts: 3

Re: quintic equation and constants

Oh, of course! I was making a really stupid mistake.
Sorry for bothering you with such a silly question!
Thank you very much for helping me! c:

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#5 2013-06-29 03:04:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,582

Re: quintic equation and constants

No bother, happens to me all the time.


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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