Math Is Fun Forum

Skymeo

Member

Registered: 2009-02-19

Posts: 2

Help with Algebra And Fractions

Friends,

Can someone please explain the Fundamental theorem Of Algebra in way that a 7th Grader can understand.Also can u guys please represent it in an algebrical form(ie:like a formula or something).Also can you guys teach me how to express a number in a continued fraction?

thanks a lot in Advance

Last edited by Skymeo (2009-03-27 04:44:10)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help with Algebra And Fractions

There's a fairly simple algorithm for making continued fractions. I'll show you with π.

So in each step, take out the integer part of the number and divide one by the rest.
You continue like that until you're bored. You can also use this method to get rational approximations of real numbers.

eg. π ≈ 3+1/7 = 22/7
      π ≈ 3+1/(7+1/16) = 355/113

In just two steps, you get a fraction which is less than a millionth away from π, and by continuing you can get as close as you want.

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Why did the vector cross the road?
It wanted to be normal.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help with Algebra And Fractions

Sometimes you can get a "recurring" continued fraction, depending on the number that you're looking at. √2 is a good example.

But you then you apply the same reasoning iteratively on (√2-1), and therefore

All square roots have "recurring" continued fractions like this, but not all of them are as easy to find.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Help with Algebra And Fractions

The fundamental theorem of algebra states that the complex field is the algebraic closure of the field of real numbers.

I’m very sorry if this doesn’t make you any wiser on the subject – but then I have no idea what “7th Grader” is.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Help with Algebra And Fractions

The fundamental theorem of algebra states that the complex field is the algebraic closure of the field of real numbers.

I’m very sorry if this doesn’t make you any wiser on the subject – but then I have no idea what “7th Grader” is.

A 7th grader is someone who is first starting to learn basic algebra.  They are understanding what it means to represent and solve an algebraic equation, must of the time linear with one variable.

As for the fundamental theorem of algebra:  If you have any polynomial at all, and the highest term which appears is x^n, then there are exactly n roots in the complex numbers, if you count roots that happen twice as being different.  For example:

(x-1)(x-1)(x-2) is a polynomial, and we say it has three roots: there are 2 one's, and one 2.  The root one is said to occur with multiplicity 2.

The fundamental theorem of algebra says that this is the case for all polynomials.  x^5 - 3x + 2 has exactly 5 roots, in the complex numbers.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."