Quote: (Originally Posted by UWSojourner)
Is there a reason not to just solve it analytically? Are there conditions that cause the analytic solution to fail?
I'm not familiar with Baker's code, but I am familiar with numerics issues. Often a root finder is used in lieu of an analytical solution because it is faster (involves fewer floating-point operations). A disadvantage of a root finder is that if you don't choose a good starting guess, you may find the wrong root. I suspect that either Baker's algorithm provides a good starting guess, or two of the roots are always complex, so that a root finder which works only with real numbers has only one root to find.