A problem by Nit Jon

Level pending

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 \(h^2\).

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