If $$\alpha$$ and $$\beta$$ are roots of the equation $$3x^2 - 13x + 14 = 0$$, then what is the value of $$(\frac{\alpha}{\beta})+(\frac{\beta}{\alpha})$$ ?

Equation : $$3x^2 - 13x + 14 = 0$$ has roots = $$\alpha$$ and $$\beta$$

Sum of roots = $$\alpha+\beta=\frac{13}{3}$$ ------------(i)

Product of roots = $$\alpha \beta=\frac{14}{3}$$ -----------(ii)

To find : $$(\frac{\alpha}{\beta})+(\frac{\beta}{\alpha})$$

= $$\frac{\alpha^2+\beta^2}{\alpha \beta}=\frac{(\alpha+\beta)^2-2\alpha \beta}{\alpha \beta}$$

Substituting values from equations (i) and (ii),

= $$[(\frac{13}{3})^2-2(\frac{14}{3})]\div(\frac{14}{3})$$

= $$(\frac{169}{9}-\frac{28}{3})\div(\frac{14}{3})$$

= $$(\frac{85}{9})\times(\frac{3}{14})$$

= $$\frac{85}{42}$$

=> Ans - (D)