If the roots of the equation $12{\mathrm{x}}^2-\mathrm{mx}+5=0$ are in the ratio $2 : 3$, then $\mathrm{m}=$

Let roots are $\mathrm{\alpha }, \mathrm{\beta }$ so, $\frac{\mathrm{\alpha }}{\mathrm{\beta }}=\frac{2}{3}\Rightarrow \mathrm{\alpha }=\frac{2\mathrm{\beta }}{3}$

$\therefore \mathrm{\alpha }+\mathrm{\beta }=\frac{\mathrm{m}}{12}$

$\Rightarrow \frac{2\mathrm{\beta }}{3}+\mathrm{\beta }=\frac{\mathrm{m}}{12}\Rightarrow \frac{5\mathrm{\beta }}{3}=\frac{\mathrm{m}}{12} ...\left(\mathrm{i}\right)$

and $\mathrm{\alpha \beta }=\frac{5}{12}\Rightarrow \frac{2\mathrm{\beta }}{3}.\mathrm{\beta }=\frac{5}{12}\Rightarrow {\mathrm{\beta }}^2=\frac{5}{8}$

$\Rightarrow \mathrm{\beta }=\sqrt{5/8}$

Put the value of $\beta$ in (i), $\left(\mathrm{i}\right), \frac{5}{3}.\sqrt{\frac{5}{8}}=\frac{\mathrm{m}}{12}\Rightarrow \mathrm{m}=5\sqrt{10}$