Formation of a Polynomial Equation from Roots

Formation of Differential Equation

Formation Of Differential Equation

Questions of matrix polynomial Equation

Formation Of Differential Equations

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Statement I If alpha_(1),alpha_(2), alpha_(3),…., alpha_(n) are the n real roots of a polynomial equation of nth degree with real coefficients such that sum of the roots taken r(1lerlen) at a time is positive, then all the roots are positive. Statement II The number of times sign of coefficients change while going left to right of a polynomial equation is the number of maximum positive roots.

Zero or Root of polynomial

Condition for Polynomial with repeated roots