CountRoots[poly, x]
gives the number of real roots of the polynomial poly in x.

CountRoots[poly, {x, a, b}]
gives the number of roots between a and b.


  • CountRoots enumerates roots with multiplicities counted.
  • Roots that lie exactly at or are counted.
  • The limits a and b can be complex, in which case the range is taken to be a closed rectangle in the complex plane.
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