JEE Advance - Mathematics (1986 - No. 8)

For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$
$$a - a\sqrt{2}$$
$$a + a\sqrt{2}$$
$$-a - a\sqrt{6}$$
$$a + a\sqrt{6}$$
$$ -a + a\sqrt{6}$$

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