Some Properties of Random Equations and their Applications to LPP

In describing a physical phenomenon, mathematical equations come to picture, whose coefficients carry some physical meanings. These coefficients of the equations are random variables following some probability distributions. Since they arise out of some experiments or natural observations, it is necessary to study the properties of the solutions of those random equations. In recent years much work has appeared on random polynomials due to its wide applications in Economics, Statistics, engineering and many other applied branches of Science. Many reputed mathematicians have developed many techniques to find out the average number of real roots for random polynomials, where the coefficients are normal or stable variables, but in our work we have concentrated our study on the average number of real roots of random algebraic polynomials when the coefficients follow different probability distributions. We have also studied the Exceedance measure of algebraic polynomials with normally distributed coefficients and their applications to linear programming problems.