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comparison of discriminant based on quadratic inequality

Source: Serbia MO 2006 2nd Grade P1

April 10, 2021
quadraticsInequalityalgebrainequalities

Problem Statement

Suppose a,b,c,A,B,Ca,b,c,A,B,C are real numbers with a≠0a\ne0 and A≠0A\ne0 such that for all xx, ∣ax2+bx+c∣≤∣Ax2+Bx+C∣.\left|ax^2+bx+c\right|\le\left|Ax^2+Bx+C\right|.Prove that ∣b2−4ac∣≤∣B2−4AC∣.\left|b^2-4ac\right|\le\left|B^2-4AC\right|.
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