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Question
If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to
Options
7/3
−7/3
3/7
-3/7
Solution
−3/7
Given equation:
\[4 x^2 + 3x + 7 = 0\]
Also,
\[\alpha\] and \[\beta\] are the roots of the equation.
Sum of the roots = \[\alpha + \beta = \frac{- \text { Coefficient of }x}{\text { Coefficient of } x^2} = - \frac{3}{4}\]
Product of the roots = \[\alpha\beta = \frac{\text { Constant term }}{\text { Coefficient of }x^2} = \frac{7}{4}\]
∴ \[\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta} = \frac{- \frac{3}{4}}{\frac{7}{4}} = - \frac{3}{7}\]
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