Question

If α, β are roots of the equation is equal to
(a) 7/3
(b) −7/3
(c) 3/7
(d) −3/7

Answer 1

(d) −3/7

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

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


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