First slide

Theory of expressions

Question

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

Moderate

A

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

$\frac{3}{7}$
C

$- \frac{3}{5}$
D

$\frac{3}{5}$

Solution

Given equation $4 x^{2} + 3 x + 7 = 0,$ therefore
$α + β = - \frac{3}{4} and αβ = \frac{7}{4}$
Now $\frac{1}{α} + \frac{1}{β} = \frac{α + β}{αβ} = \frac{- 3 / 4}{7 / 4} = \frac{- 3}{4} \times \frac{4}{7} = - \frac{3}{7} .$

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