If `alpha, beta gamma` are the real roots of the equation `x^(3)-3px^(2)+3qx-1=0`, then find the centroid of the triangle whose vertices are `(alpha, (1)/(alpha)), (beta, (1)/(beta))` and `(gamma, (1)/(gamma))`.

Options

A. (a,b)
B. (a/3,b/3)
C. (a+b,a-b)
D. (3a,3b)

Answer

A

Explanation

We have
`alpha+beta+gamma=3a, alpha beta+beta gamma+gamma alpha=3b and alpha beta gamma=1`
The centroid of the given triangle is at the point
`((alpha+beta+gamma)/(3),((1)/(alpha)+(1)/(beta)+(1)/(gamma))/(3))=((alpha+beta+gamma)/(3),(alpha beta+beta gamma+gamma beta)/(2alpha beta gamma))=(a,b)`