Question

If $\alpha ,\beta$ are roots of the equation $4x^2+3x+7=0,$ then~,

$\frac{1}{\alpha }+\frac{1}{\beta }$ is equal to

Answer 1

$\text{Given equation:}4x^2+3x+7=0,\text{Also,}\alpha and\beta \text{are the roots of the equation.}\text{Sum of the roots}=\alpha +\beta =\frac{-coefficientofx}{coefficientof{x}^2}=-\frac{3}{4}\text{Product of the roots}\alpha \beta \frac{-coefficientterm}{coefficientof{x}^2}=\frac{7}{4}\therefore then,\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{\frac{-3}{4}}{\frac{7}{4}}=-\frac{3}{7}$