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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb36f556a-4446-44b1-8397-48d6cb78d512%2F3c055440-b92a-4191-8d3b-8d12b98c9cd2%2Fn4bci9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
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