Using Sturms Technique to Find the Polynomials Real Roots

The mathematician Jack Storm made an effort to obtain the most important method through which he allowed us to calculate the number of distinct real roots of the polynomial. This technique is used to calculate the total (distinct) number of real roots or just count the number of roots presented in a time period. In this work, we use the Sturm scheme for finding the real roots of nonlinear functions, whether we can define them as periodic or aperiodic. By keeping some of the research conditions on the practical side, we come up with promising solutions that do the trick, paying attention to Descartes' rule of signs, which will inform us of the existence of the solution when the signs change.