Question

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

• A. $5\sqrt{10}$
• B. $3\sqrt{10}$
• C. $2\sqrt{10}$
• D. None of these

Answer 1

The correct option is A $5\sqrt{10}$

Let roots are $\alpha ,\beta so,\frac{\alpha }{\beta }=\frac{2}{3}\Rightarrow \alpha =\frac{2\beta }{3}$
$\therefore \alpha +\beta =\frac{m}{12}$
$\Rightarrow \frac{2\beta }{3}+\beta =\frac{m}{12}\Rightarrow \frac{5\beta }{3}=\frac{m}{12}........\left(i\right)$
and $\alpha \beta =\frac{5}{12}\Rightarrow \frac{2\beta }{3}.\beta =\frac{5}{12}\Rightarrow {\beta }^2=\frac{5}{8}$
$\Rightarrow \beta =\sqrt{\frac{5}{8}}$
Put the value of $\beta$ in $\left(i\right),\frac{5}{3}.\sqrt{\frac{5}{8}}=\frac{m}{12}\Rightarrow m=5\sqrt{10}$.