If the equation 2x2 - 7x + 12 = 0 has two roots and , then the value of / + / \, is?

Answer: Option B

$$\begin{array}{rl}& \text{2}{x}^2-7x+12=0\\ & \text{roots are }\alpha \text{ , }\beta \\ & \therefore \alpha \beta =+\frac{c}{a},\alpha +\beta =\frac{-b}{a}\\ & \therefore \alpha +\beta =+\frac{7}{2},\alpha \beta =\frac{12}{2}=6\\ & \therefore \frac{\alpha }{\beta }+\frac{\beta }{\alpha }\\ & =\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }\\ & =\frac{{\left(\alpha +\beta \right)}^2-2\alpha \beta }{\alpha \beta }\\ & =\frac{{\left(\frac{7}{2}\right)}^2-2\times 6}{6}\\ & =\frac{\frac{49}{4}-12}{6}\\ & =\frac{49-48}{6\times 4}\\ & =\frac{1}{24}\end{array}$$