Question

If one of roots of $x^2+ax+4=0$ is twice the other root, then the value of 'a' is .

• A. $-3\sqrt{2}$
• B. $8\sqrt{2}$
• C. $\sqrt{2}$
• D. $-2\sqrt{2}$

Answer 1

The correct option is A $-3\sqrt{2}$

Let $m$ and $2m$ be the roots of the equation.

Then product of the roots is $2m^2=4$

$\Rightarrow$ $m^2=2$

$\Rightarrow$ $m=\pm \sqrt{2}$

Sum of the roots is $m+2m=3m=3(\pm \sqrt{2})$

For instance let us consider positive square root i.e. $m=\sqrt{2}$

Then sum of the roots=$-a=3\sqrt{2}$

$\Rightarrow$ $a=-3\sqrt{2}$

$\therefore$ Option A is correct.