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Evaluating a quartic polynomial.

  1. May 18, 2012 #1
    I want to find the root(for N) of this equation:

    [tex] \frac{(2N-1)^2}{N(1-N)}=Ce^t [/tex]

    The hint says "consider taking a substitution u=N-1/2" ...which is the top bit of the fraction. But what does take a substitution here mean ?

    This is a part of a loooong modelling problem which involved an ugly *** integral and gave this equation as the result. I've never evaluated a "quartic equation" so I'm a bit confused about the process.

    I have the answer from wolfram so am looking for guidance on how to work it out by hand.
     
  2. jcsd
  3. May 18, 2012 #2

    sharks

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    Gold Member

    [tex]\frac{(2N-1)^2}{N(1-N)}=Ce^t[/tex]For the numerator, use the substitution:
    [tex]2N-1=2u[/tex]For the denominator, use the substitution:
    [tex]N=\frac{2u+1}{2}[/tex]
     
  4. May 18, 2012 #3

    Ray Vickson

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    What is stopping you from substituting N = u + 1/2 into the expression on the left? It is simple algebra. If you actually DO it you will see how to proceed.

    RGV
     
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