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

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(a, b)

(a/3, b/3)

(a+b, a−b)

(3a, 3b)

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detailed solution

Correct option is A

We haveα+β+γ=3a,αβ+βγ+γα=3b and αβγ=1The centroid of the given triangle is at the pointa+β+γ3,1α+1β+1γ3=α+β+γ3,αβ+βγ+γα3αβγ=(a,b)

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If α, β, γ are the real roots of the equation x2−3ax2+3bx−1=0 then the centroid of the triangle with metrices α,1α, β,1β and γ,1γis at the point

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