MathDB

p(x) = x^3 + Ax^2 + Bx +C has 3 roots, at least 2 distinct then A^2+B^2+18C>0

Source: Germany 1996 p6a

February 22, 2020

polynomialrootsalgebra

Problem Statement

Prove the following statement: If a polynomial

p(x) = x^3 + Ax^2 + Bx +C

has three real positve roots at least two of which are distinct, then

A^2 +B^2 +18C > 0