The distance of three points A, B, C on a straight line from a fixed origin O on the line are the roots of the equation ax^3+3bx^2+3cx+d=0 . Find the

The distance of three points A, B, C on a straight line from a fixed origin O on the line are the roots of the equation ax^3+3bx^2+3cx+d=0 . Find the condition that is of the point A, B, C should bisect the distance between the other two.?
 
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