Let f(x)= Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A, A + B and C are all integers. Conversely, prove that if the number 2A, A + B and C are all integers then f(x) is an integer whenever x is an integer.
Let f(x)= Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A, A + B and C are all integers. Conversely, prove that if the number 2A, A + B and C are all integers then f(x) is an integer whenever x is an integer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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