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(6x^2 -24x -4a) and (x^3 + ax^2 + bx - 8) have non-negative real roots

Source: Estonia IMO TST 2005 p4

March 28, 2020

polynomialalgebraReal Roots

Problem Statement

Find all pairs

(a, b)

of real numbers such that the roots of polynomials

6x^2 -24x -4a

and

x^3 + ax^2 + bx - 8

are all non-negative real numbers.