MathDB

Polynomial Relationships

Source: MOP 2002

July 12, 2008

algebrapolynomialquadraticsquadratic formula

Problem Statement

The polynomial P(x)\equal{}x^3\plus{}ax^2\plus{}bx\plus{}d has three distinct real roots. The polynomial

P(Q(x))

, where Q(x)\equal{}x^2\plus{}x\plus{}2001, has no real roots. Prove that

P(2001)>\frac{1}{64}