Sturm’s theorem

Sturm's theorem is a mathematical theorem that determines the number and position of real roots for an algebraic equation within specified limits. Developed by French mathematician Charles-Fran\u00e7ois Sturm, it provided a complete solution to a problem that had been explored since the time of Ren\u00e9 Descartes. The theorem is crucial for understanding the behavior of equations and finding their solutions. Sturm also made significant contributions to the theory of differential equations, working with Joseph Liouville on problems related to heat conduction. Their work led to the Sturm-Liouville problem, a class of partial differential equations with boundary conditions commonly used in physics and quantum mechanics.123