Question: Robustness of plot(eval(something,[])) vs implicitplot3d(something) and slider's precision in Explore()?


I want to analyze a quartic equation: I am interested in positive roots, which I need expressed in explicit/closed form.

I include four questions in the script.


EDIT (since my question was originally tagged as incomplete and even duplicate):
Above all I am trying to understand:

  1. Why implicitplot3d returns a unique strictly positive root for all rho and Gamma but plot() of the quartic evaluated for a specific pair of value returns three positive roots?
  2. rho is a correlation coefficient, thus bounded in (-1,+1): how to adjust the precision of the slider in Explore() so that I can play around with multiple rho values within said range?
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