Question

If $\alpha ,\beta$ are the roots of the equation $2x^2+3x+7=0$, find $\frac{1}{\alpha }+\frac{1}{\beta }$

• A. $\frac{-3}{5}$
• B. $\frac{3}{7}$
• C. $\frac{-3}{7}$
• D. None

Answer 1

The correct option is C $\frac{-3}{7}$

Here, $\alpha$ and $\beta$ are roots of the equation $2x^2+3x+7=0$

$\Rightarrow$ $\alpha +\beta =\frac{-b}{a}=\frac{-3}{2}$ ---- ( 1 )

$\Rightarrow$ $\alpha \beta =\frac{c}{a}=\frac{7}{2}$ ---- ( 2 )

$\Rightarrow$ $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }$

$=\frac{\frac{-3}{2}}{\frac{7}{2}}$ [ From ( 1 ) and ( 2 ) ]

$=\frac{-3}{7}$

$\therefore$ $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{-3}{7}$