Math Is Fun Forum

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:

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: quintic equation and constants

hi romani

Welcome to the forum.

This involves the binomial theorem.  Do you know this?

Bob

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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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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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.

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:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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