Fractional index

For discussing Olympiad Level Algebra (and Inequality) problems
ahmedulkavi
Posts:14
Joined:Tue Feb 01, 2011 11:20 am
Fractional index

Unread post by ahmedulkavi » Wed Feb 23, 2011 10:53 am

There is a theorem that n powered equation have n roots.
But this equation:
root over x or x^1/2=4 should have 1/2 roots but it have one root , 16.
another example is,
x^3/2=2^3/2 should have 3/2 roots but it has one root, 2
It creates problem if we factorise this equation like this:
x^3-8=0 into [x^3/2-2^3/2][x^3/2+2^3/2]=0
But it gives two roots,2and -2 while -2 is not the real root.
Why is this happened?

HandaramTheGreat
Posts:135
Joined:Thu Dec 09, 2010 12:10 pm

Re: Fractional index

Unread post by HandaramTheGreat » Wed Feb 23, 2011 11:33 am

code of $\sqrt{x}$ is \sqrt{x} ... just put two dollar sign in both side of it...
code of $x^2$ is x^2...
you can also see the code by double clicking on a LaTeXed equation...
writing without LaTeX looks like a mess and many wouldn't like to read 'em...

tanvirab
Posts:446
Joined:Tue Dec 07, 2010 2:08 am
Location:Pasadena, California, U.S.A.

Re: Fractional index

Unread post by tanvirab » Fri Feb 25, 2011 12:06 am

Polynomials of degree $n$ have $n$ roots. Polynomials have only nonnegative integer powers of the variable. If you have fractional powers than it's not a polynomial anymore.

For your second question, $(-2)^{3/2}$ is not a real number. So, $-2$ is not a solution even after you factorize it. You have to be careful when you take fractional power.

Post Reply