Question

If α, β are roots of the equation \[4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta\] is equal to

पर्याय

• 7/3

• −7/3

• 3/7

• -3/7

Answer 1

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

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