If alpha, beta, gamma are real roots of the equation x3 - 3px2+ 3px -1= 0, then find the centroid - Maths -

Question

If alpha, beta, gamma are real roots of the equation x3
- 3px​2+ 3px -1= 0, then find the centroid of a
triangle whose vertices are (alpha, 1/alpha) , (beta, 1/beta) and
(gamma, 1/gamma)

Rishabh Mittal · Accepted Answer

Dear Student ,
Please find below the solution to the asked query :

x3-3px2+3px-1=0Roots are α , β and γ 
Now ,α+β+γ=--3p1=3pαβ+βγ+γα=3p1=3pαβγ=--11=1Vertices of triangle are α,1α , β,1β , γ,1γCentroid of a triangle α+β+γ3 , 1α+1β+1γ3=α+β+γ3,βγ+αγ+αβ3 αβγ=3p3,3p31=p , p    ANS
Centroid of a triangle is p,p 
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If alpha, beta, gamma are real roots of the equation x3 - 3px​2+ 3px -1= 0, then find the centroid of a triangle whose vertices are (alpha, 1/alpha) , (beta, 1/beta) and (gamma, 1/gamma).

If alpha, beta, gamma are real roots of the equation x³ - 3px²+ 3px -1= 0, then find the centroid of a triangle whose vertices are (alpha, 1/alpha) , (beta, 1/beta) and (gamma, 1/gamma).