olymmath

Putnam 2003 A4

  • Session A

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

Dataset text Putnam 1995 to 2025. Quoted with source.

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