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2014 AIME I Question 6

AIME · 2014 AIME I

Question 6

The graphs $y = 3(x-h)^2 + j$ and $y = 2(x-h)^2 + k$ have $y$-intercepts of $2013$ and $2014,$ respectively, and each graph has two positive integer $x$-intercepts. Find $h.$