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Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
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Why does Solve produce a result in terms of one variable, but not the other?
I have the following quartic equation:\begin{equation}
x^4 + ax^3 + bx^2 + ax + 1 = 0
\end{equation} and I'm trying to find relations for $a$ and $b$ for which we have multiple roots. To this end, I s …