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