Question

If $\alpha and\beta$ are the roots of the equation $4x^2+3x+7=0$, then $\frac{1}{\alpha }+\frac{1}{\beta }=$

• A. $-\frac{3}{7}$
• B. $\frac{3}{7}$
• C. $-\frac{3}{5}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A

$-\frac{3}{7}$

Given equation $4x^2+3x+7=0$, $\therefore$

$\alpha +\beta =-\frac{3}{4}and\alpha \beta =\frac{7}{4}$

Now $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{\frac{-3}{4}}{\frac{7}{4}}=\frac{-3}{4}\times \frac{4}{7}=-\frac{3}{7}$