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The set of all \mathrm{a \: \epsilon \: R } for which the equation \mathrm{x |x -1| + |x + 2| + a= 0} has exactly one real root, is
 

Option: 1

\left ( -\infty ,-3 \right )


Option: 2

\left ( -\infty ,\infty \right )


Option: 3

\left ( -6,\infty \right )


Option: 4

\left ( -6,-3 \right )


Answers (1)

best_answer

\mathrm{f\left ( x \right )=x\mid\: x-1\mid+\mid\: x+2\mid}

\mathrm{x\mid\: x-1\mid+\mid\: x+2\mid+a=0}

\mathrm{x\mid\: x-1\mid+\mid\: x+2\mid-a}

All values are increasing.

Posted by

Pankaj Sanodiya

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