Question

$If\alpha ,\beta ,\gamma arerootsequation{x}^3+a{x}^2+bx+c=0,then{\alpha }^{-1}+{\beta }^{-1}+{\gamma }^{-1}=$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\alpha ,\beta ,\gamma$ are the roots of the equation

$x^3+a{x}^2+bx+c=0so\alpha +\beta +\gamma =-a,\alpha \beta +\beta \gamma +\gamma \alpha =band\alpha \beta \gamma =-cnow{\alpha }^{-1}+{\beta }^{-1}+{\gamma }^{-1}=\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=\frac{\alpha \beta +\beta \gamma +\gamma \alpha }{\alpha \beta \gamma }=-\frac{b}{c}$