MathDB
Roots of Quadratic are Integers

Source: 2015 AMC 12A #18/10A #23

February 4, 2015
quadraticsfunctionalgebrapolynomialVietaSFFTAMC

Problem Statement

The zeroes of the function f(x)=x2ax+2af(x)=x^2-ax+2a are integers. What is the sum of all possible values of aa?
<spanclass=latexbold>(A)</span>7<spanclass=latexbold>(B)</span>8<spanclass=latexbold>(C)</span>16<spanclass=latexbold>(D)</span>17<spanclass=latexbold>(E)</span>18<span class='latex-bold'>(A) </span>7\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>16\qquad<span class='latex-bold'>(D) </span>17\qquad<span class='latex-bold'>(E) </span>18