Question

If roots of the equation $12x^2+mx+5=0$ are in the ratio $3:2$, 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 $5\sqrt{10}$

Given equation:

$12x^2+mx+5=0$

The roots are in ratio $3:2$

Hence,let roots of the equations are $3\alpha$ and $2\alpha .$

Applying condition for sum and product of the roots,

$3\alpha +2\alpha =-\frac{m}{12}$ and

$3\alpha \times 2\alpha =\frac{5}{12}$

$\Rightarrow {\alpha }^2=\frac{5}{72}$

$\Rightarrow \alpha =\pm \frac{\sqrt{5}}{6\sqrt{2}}$

And

$m=-60\alpha$

$\Rightarrow m=\pm 5\sqrt{10}$

Hence, A is the correct option.