Question:
If $\alpha, \beta$ are roots of the equation $4 x^{2}+3 x+7=0$, then $1 / \alpha+1 / \beta$ is equal to
(a) 7/3
(b) −7/3
(c) 3/7
(d) −3/7
Solution:
(d) −3/7
Given equation: $4 x^{2}+3 x+7=0$
Also, $\alpha$ and $\beta$ are the roots of the equation.
Sum of the roots $=\alpha+\beta=\frac{-C \text { oefficient of } x}{C \text { oefficient of } x^{2}}=-\frac{3}{4}$
Product of the roots $=\alpha \beta=\frac{C \text { onstant term }}{C \text { oefficient of } x^{2}}=\frac{7}{4}$
$\therefore \quad \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{-\frac{3}{4}}{\frac{7}{4}}=-\frac{3}{7}$