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The roots z(1),z(2) " and " z(3) of the ...

The roots `z_(1),z_(2) " and " z_(3)` of the equation `x^(3)+3ax^(2)+3bx+c=0` in which a,b and c are complex numbers, correspond to the points A,B,C on the Gaussian plane. Find the centroid of the `/_\ABC` and show that it will be equilateral, if` `a^(2)=b`.

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