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#1 2013-06-29 03:51:45

romani
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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:

#2 2013-06-29 04:05:39

bob bundy
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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

#3 2013-06-29 04:21:04

bobbym
Administrator

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#4 2013-06-30 01:02:33

romani
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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:

#5 2013-06-30 01:04:27

bobbym
Administrator

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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