AMC 12A 2014 Problem 19

Past Contests AMC 12 AMC 12A - 2014
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1

There are exactly N distinct rational numbers k such that |k|<200 and

5 x^{2}+k x+12=0

has at least one integer solution for x. What is N ?

Answer Choices
A. 6
B. 12
C. 24
D. 48
E. 78