If α, β are roots of the equation
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 $=\alpha \beta=\frac{C \text { onstant term }}{C \text { oefficient of } x^{2}}=\frac{7}{4}$

$\therefore \quad \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{-\frac{3}{4}}{\frac{7}{4}}=-\frac{3}{7}$

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