JEE Advance - Mathematics (1986 - No. 8)

For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$

$$a - a\sqrt{2}$$

$$a + a\sqrt{2}$$

$$-a - a\sqrt{6}$$

$$a + a\sqrt{6}$$

$$ -a + a\sqrt{6}$$