If α,β,γ are the real roots of the equation x3−3px2+3qx−1=0 then the centroid of the triangle with vertices α,1α,β,1β and γ,1γ
is at the point
(p, q)
(p/3, q/3)
(p + q.p - q)
(3p, 3q)
The centroid of the given triangle is the point
α+β+γ3,1α+1β+1γ3=3p3,αβ+βγ+γα3αβγ
=(p,q)[∵α+β+γ=3p,αβ+βγ+γα=3q,αβγ=1]