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

पर्याय

• \[\frac{4}{7}\]

• \[- \frac{3}{7}\]

• \[\frac{3}{7}\]

• \[- \frac{3}{4}\]

Answer 1

 −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 = \[\alpha\beta = \frac{\text { Constant term }}{\text { Coefficient of } x^2} = \frac{7}{4}\]

\[\therefore \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta} = \frac{- \frac{3}{4}}{\frac{7}{4}} = - \frac{3}{7}\]