If  α,β,γ,are the roots of x3−2x2−5x+6=0, the orthocenter of the triangle with  vertices α,β,γ, β,γ,α, γ,α,β  is

The vertices ,  α,β,γ, β,γ,α, γ,α,β forms an equilateral triangle, so the orthocenter of the triangle coincide with centroid. Hence the ortho center is  α+β+γ3,α+β+γ3,α+β+γ3When   α,β,γare the roots of x3−2x2−5x+6=0, sum of the roots is α+β+γ=2Therefore, the ortho center is  23,23,23