Question

If $\alpha ,\beta ,\gamma$ are the roots of the equation $2x^3-5x^2+3x-1=0,$ then $\frac{1}{\alpha \beta }+\frac{1}{\beta \gamma }+\frac{1}{\gamma \alpha }=$

• A. $4$
• B. $-5$
• C. $5$
• D. $-4$

Answer 1

The correct option is C $5$

The required expression can be written as $\frac{\alpha +\beta +\gamma }{\alpha \beta \gamma }$
Now, $\alpha +\beta +\gamma =\frac{5}{2}$ and $\alpha \beta \gamma =\frac{1}{2}.$
So the value of the given expression is $\frac{\frac{5}{2}}{\frac{1}{2}}=5.$