If $α$ and $β$ are the roots of the quadratic equation $4 x^{2} + 3 x + 7 = 0$ , then the value of $\frac{1}{α} + \frac{1}{β}$ is:

- \frac{3}{4}

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- \frac{3}{7}

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\frac{3}{7}

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\frac{4}{7}

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Solution

The correct option is A $- \frac{3}{7}$
If $α, β$ are the roots of quadratic $4 x^{2} + 3 x + 7 = 0$ , then

$α + β = - \frac{3}{4}$ and $α β = \frac{7}{4}$

Hence $\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- 3}{4} \times \frac{4}{7}$

$= - \frac{3}{7}$

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