Question

If the roots of the equation $12x^2+mx+5=0$ are in the ratio $5:4$, then $m=$

• A. $9\sqrt{3}$
• B. $\pm 9\sqrt{3}$
• C. $6\sqrt{3}$
• D. $\pm 6\sqrt{3}$

Answer 1

Answer: (B)

$\pm 9\sqrt{3}$

Let the roots be $\alpha ,\beta$
$\frac{\alpha }{\beta }=\frac{5}{4}\Rightarrow \alpha =\frac{5\beta }{4}$ & $\frac{\alpha +\beta }{\beta }=\frac{9}{4}$
$\alpha +\beta =\frac{-b}{a}=\frac{-m}{12}=\frac{9\beta }{4}$
$m=-27\beta$
$\alpha \beta =\frac{c}{a}=\frac{5{\beta }^2}{4}=\frac{5}{12}$
$\beta =\pm \frac{1}{\sqrt{3}}$
$\therefore m=-27\beta =-27\times \pm \frac{1}{\sqrt{3}}$
$m=\pm 9\sqrt{3}$