Author 
Comment/Response 
jayjay

04/18/13 1:31pm
up vote 0 down vote favorite
I am very new to Mathematica, and I am trying to solve the following problem.
I have a cubic equation of the form Z = aZ^3 + bZ^2 + a + b. The first thing I want to do is to get a function that solves this analytically for Z and chooses the minimal positive root for that, as a function of a and b.
I thought that in order to get the root I could use:
Z = Solve[z == az^3 + bz^2 + a + b, z]
It seems like I am not quite getting the roots, as I would expect using the general cubic equation solution formula.
I want to integrate the minimal positive root of Z over a and b (again, preferably analytically) from 0 to 1 for a and for a to 1 for b.
I tried
Y = Integrate[Z, {a, 0, 1}, {b, a, 1}]
and that does not seem to give any formula or numerical value, but just returns an integral. (notice I am not even sure how to pick the minimal positive root, but I am playing around with Mathematica to try to figure it out.)
Any ideas how to do this?
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