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