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Integer Solution

Source: 2014 AMC 12A #19

February 5, 2014
AMCAIMEsymmetryalgebrapolynomialVietaAIME I

Problem Statement

There are exactly NN distinct rational numbers kk such that ∣k∣<200|k|<200 and 5x2+kx+12=05x^2+kx+12=0 has at least one integer solution for xx. What is NN?
<spanclass=′latex−bold′>(A)</span>6<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>24<spanclass=′latex−bold′>(D)</span>48<spanclass=′latex−bold′>(E)</span>78<span class='latex-bold'>(A) </span>6\qquad <span class='latex-bold'>(B) </span>12\qquad <span class='latex-bold'>(C) </span>24\qquad <span class='latex-bold'>(D) </span>48\qquad <span class='latex-bold'>(E) </span>78\qquad
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