2012 AIME I Problem 14

Complex numbers a, b, and c are the zeros of a polynomial P(z)=z^{3}+ q z+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}.