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st: How to obtain the solution of a quintic polynomial equation using Stata


From   tiago.pereira@incor.usp.br
To   statalist@hsphsun2.harvard.edu
Subject   st: How to obtain the solution of a quintic polynomial equation using Stata
Date   Sat, 17 Nov 2007 15:11:35 -0200 (BRT)

Dear Statalisters

I have the following quintic polynomial equation
dy=a0+a1*x+a2*x^2+a3*x^3+a4*x^4+a5*x^5

the objective is to estimate x.

where

a0= x12*mu_s*(1+mu_s)+2*x22*mu_s^2
a1=-2*(n*mu_s*(1+mu_s)+x12*mu_s)
a2=6*n*mu_s+2*x11+x12
a3=-2*(2*n*mu_s+n+2*x11+x12)
a4=4*n+2*x11+x12
a5=-2*n

Is there a straighforward way to solve it using Stata? Or, since I know
that x is constrained between 0 and 1, to use brute force to find out the
solution? If so, how many decimals places used in a loop would you
suggest?

Tiago

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