Question

If α,β,γ are the roots of $x3$+p$x^2$+qx+r=0 , then (α- $\frac{1}{\beta \gamma }$) (β – $\frac{1}{\gamma \alpha }$) (γ – $\frac{1}{\alpha \beta }$) =

• A. - (r + 1)³ / r²
• B. (r³ - 1)/r²
• C. (r³ + 1)/r²
• D. None of these

Answer 1

The correct option is A

- (r + 1)³ / r²

αβγ= -r

(α- $\frac{1}{\beta \gamma }$) (β – $\frac{1}{\gamma \alpha }$) (γ – $\frac{1}{\alpha \beta }$)

=$\frac{(\alpha \beta \gamma -1{)}^3}{(\alpha \beta \gamma {)}^2}$ = $\frac{-(r+1{)}^3}{r^2}$