# square root function

• September 16th 2011, 04:23 PM
Veronica1999
square root function
Hmm...I can't see what the significance of the the first quadrant point is...
• September 16th 2011, 10:32 PM
CaptainBlack
Re: square root function
Quote:

Originally Posted by Veronica1999
Hmm...I can't see what the significance of the the first quadrant point is...

The $x$ coordinate is the solution of the equation $f(x)=x$ which may be expanded:

$\sqrt{1996x}=x^2$

and again:

$1996x=x^4$

(but now we need to remember that $x\ge 0$) and rearranging we have:

$x^4-1996x=0$

which by Descartes rule of signs has exactly one positive root. So the $x$ coordinate of the point of intersection is the unique positive root of the quartic:

$x^4-1996x=0$

CB