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Math Help - square root function

  1. #1
    Member Veronica1999's Avatar
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    square root function

    Hmm...I can't see what the significance of the the first quadrant point is...
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  2. #2
    Grand Panjandrum
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    Re: square root function

    Quote Originally Posted by Veronica1999 View Post
    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
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