Question

If α and β are the roots of $4x^2+3x+7=0$, then the value of $\frac{1}{\alpha }+\frac{1}{\beta }$ is
(a) $\frac{4}{7}$
(b) $-\frac{3}{7}$
(c) $\frac{3}{7}$
(d) $-\frac{3}{4}$

Answer 1

(b) −3/7

Given equation: $4x^2+3x+7=0$
Also, $\alpha$ and $\beta$ are the roots of the equation.

Then, sum of the roots = $\alpha +\beta =\frac{-C\mathrm{oefficient}\mathrm{of}x}{C\mathrm{oefficient}\mathrm{of}{x}^2}=-\frac{3}{4}$

Product of the roots = $\alpha \beta =\frac{C\mathrm{onstant}\mathrm{term}}{C\mathrm{oefficient}\mathrm{of}{x}^2}=\frac{7}{4}$

$\therefore \frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{-{\displaystyle \frac{3}{4}}}{{\displaystyle \frac{7}{4}}}=-\frac{3}{7}$