[JEE Advanced 1986] For $a\le0$, determine all real roots of $x^2-2a|x-a|-3a^2=0$.
For $a\le0$, determine all real roots of $x^2-2a|x-a|-3a^2=0$.
1 Answer
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Answer: $x=(1-\sqrt2)\,a$ and $x=(\sqrt6-1)\,a$.
For $x\ge a$: $x^2-2ax-a^2=0\Rightarrow x=(1-\sqrt2)a$ (the root satisfying $x\ge a$). For $x<a$: $x^2+2ax-5a^2=0\Rightarrow x=(\sqrt6-1)a$.
JEE Advanced 1986 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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