If the equation $2x^2-7x+12 =0$ has two roots $\alpha$ and $\beta$ ,
then the value of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$ is
note $x=\frac{-7+\sqrt{47}}{4},\frac{-7-\sqrt{47}}{4}$
then
$$\frac{\frac{-7+\sqrt{47}}{4}}{\frac{-7-\sqrt{47}}{4}}+\frac{\frac{-7-\sqrt{47}}{4}}{\frac{-7+\sqrt{47}}{4}}$$
so 96/2
Best Answer
$\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}$
since $\alpha+\beta=\frac{7}{2}$ and $\alpha\beta=6$, you can compute the value by substituting.