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Evaluating a quartic polynomial.

  • Thread starter sid9221
  • Start date
111
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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.
 

DryRun

Gold Member
837
3
[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]
 

Ray Vickson

Science Advisor
Homework Helper
Dearly Missed
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1,710
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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