Question: If α, β, γ are the real roots of the equation, x<sup>3</sup> – 3px<sup>2</sup> + 3qx – 1 = 0, the c...

Question

If α, β, γ are the real roots of the equation,

x³ – 3px² + 3qx – 1 = 0, the centroid of the triangle whose vertices are $\left( \alpha,\frac{1}{\alpha} \right)$ , $\left( \beta,\frac{1}{\beta} \right)$ , $\left( \gamma,\frac{1}{\gamma} \right)$ is

Answer 1

Solution

∴ α + β + γ = 3p ; αβ + αα + βγ = 3q ; αβγ = 1