KnowraSturm's theoremLinked fromLinked fromThe 4 pages that link to Sturm's theorem, each with the reason it gives.All 4Related 2Compared with 2Discriminant (polynomial)Related: Discriminant-zero parameter values mark where real roots can merge as coefficients vary.Descartes' rule of signsCompared with: It can determine exact interval root counts when Descartes' rule gives only an upper bound.Budan's theoremCompared with: Sturm's later method sharpened interval root counting beyond Budan's upper-bound approach.Four-vertex theoremRelated: Related zero-counting ideas help establish lower bounds on curvature extrema.