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If $α, β, γ$ are the real roots of the equation $x^{3} - 3 {px}^{2} + 3 qx - 1 = 0$ then the centroid of the triangle with vertices $(α, \frac{1}{α}), (β, \frac{1}{β}) and (γ, \frac{1}{γ})$
is at the point

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(p, q)

(p/3, q/3)

(p + q.p - q)

(3p, 3q)

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detailed solution

Correct option is A

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]

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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

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Ready to Test Your Skills?

free study material

If $α, β, γ$ are the real roots of the equation $x^{3} - 3 {px}^{2} + 3 qx - 1 = 0$ then the centroid of the triangle with vertices $(α, \frac{1}{α}), (β, \frac{1}{β}) and (γ, \frac{1}{γ})$
is at the point