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The roots z1, z2, z3 of the equation z^3...

The roots `z_1, z_2, z_3 `of the equation `z^3+3alpha z^2+ 3betaz+gamma=0 `correspond to the points A, B and C on the complex plane. Find the complex number representing the centroid of the triangle ABC, and show that the triangle is equilateral if `alpha^2=beta`

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