# Problem #1836

 1836 There are exactly $N$ distinct rational numbers $k$ such that $|k|<200$ and $$5x^2+kx+12=0$$ has at least one integer solution for $x$. What is $N$? $\textbf{(A) }6\qquad \textbf{(B) }12\qquad \textbf{(C) }24\qquad \textbf{(D) }48\qquad \textbf{(E) }78\qquad$ This problem is copyrighted by the American Mathematics Competitions.
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