Inverse of a quartic equation

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p=ax^3+bX^2+cX is positive monotonic and has an inverse X=G(p)

But I can't invert it. Is there an analytic solution?
For given parameter values I can plot numeric values- it has a tilted S shape.
 

Answers and Replies

  • #2
HallsofIvy
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This is, by the way, a "cubic" equation, not "quartic". I take it, you mean by "is positive monotonic" that you are assuming values of a, b, and c such that the function is monotonic. Of course a cubic equation cannot always be positive. A true "quartic" (fourth degree) equation can but it cannot be monotonic.

There is a general formula for solutions to cubic equations that could, theoretically, give an inverse function for this, but it is extremely complicated.
 

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