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Putnam 2003 A4

Source:

June 23, 2011
Putnamquadraticsfunctioncalculusderivativeinequalitiesabsolute value

Problem Statement

Suppose that a,b,c,A,B,Ca, b, c, A, B, C are real numbers, a≠0a \not= 0 and A≠0A \not= 0, such that ∣ax2+bx+c∣≤∣Ax2+Bx+C∣|ax^2+ bx + c| \le |Ax^2+ Bx + C| for all real numbers xx. Show that ∣b2−4ac∣≤∣B2−4AC∣|b^2- 4ac| \le |B^2- 4AC|
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