2012 AIME I Problem 14

Complex numbers a, b, and c are zeros of a polynomial P(z) = z^3 + qz + r, and |a|^2 + |b|^2 + |c|^2 = 250. The points corresponding to a, b, and c in the complex plane are the vertices of a right triangle with hypotenuse h. Find h^2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.