Question

If the roots of the equation $4x^2+ax+3=0$ are in ratio of $1:2$, then value(s) of $a$ is/are

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

Answer 1

Answer: (B), (D)

$3\sqrt{6}$

Let the roots of the equation be $l,m$, then
$m=2l\cdots \left(1\right)$
Now, the product of the roots,
$lm=\frac{3}{4}$
Using equation $\left(1\right)$,
$\Rightarrow 2l^2=\frac{3}{4}\Rightarrow l=\pm \frac{\sqrt{3}}{2\sqrt{2}}\cdots \left(2\right)$
Sum of the roots is,
$l+m=-\frac{a}{4}\Rightarrow -\frac{a}{4}=3l\therefore a=\mp 3\sqrt{6}$