Question

If α and β are the roots of the equation $3x^2+8x+2=0,\mathrm{then}\left(\frac{1}{\alpha }+\frac{1}{\beta }\right)=?$
(a) $\frac{-3}{8}$
(b) $\frac{2}{3}$
(c) −4
(d) 4

Answer 1

(c) −4

$$\begin{gathered} \text{Given:} \\ \alpha \text{and}\beta \text{are the roots of the equation 3}{x}^2+8x+2=0 \\ \therefore \alpha +\beta =\frac{-8}{3}\text{and}\alpha \beta \text{=}\frac{2}{3}\text{...(i)} \\ \therefore \left(\frac{1}{\alpha }+\frac{1}{\beta }\right)=\left(\frac{\alpha +\beta }{\alpha \beta }\right) \\ =\frac{\left(\frac{-8}{3}\right)}{\left(\frac{2}{3}\right)}(\mathrm{from}(\mathrm{i}\left)\right) \\ \begin{array}{l}=\frac{-8}{2}\end{array} \\ =-4 \end{gathered}$$