Dominant balance for algebraic roots
= Dominant balance for algebraic roots
{title2=$t=\epsilon^p s$}
For a polynomial depending on a small parameter, substitute $t=\epsilon^p s$ and compare the exponents of the parameter. Candidate root scales arise when two or more lowest exponents balance. Solve the leading scaled equation and expand about each of its nonzero roots. Different balances can reveal different families of roots; real-root counts must be checked separately.