Answer :

given |2x-x2-3| = 1

2x-x2-3 = ±1


When 2x-x2-3 = 1


2x-x2-3 -1 = 0


2x-x2-4 = 0


= x2 – 2x +4 = 0


Discriminant, D = 4 - 16


= -12 < 0


Hence the roots are unreal.


When 2x-x2-3 = -1


= x2 – 2x -2 = 0


Discriminant, D = 4 – 8 = - 4 < 0


Hence the roots are unreal.


Hence the given equation has no real roots.

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