The number of real roots of the equation x|x| - 5|x + 2| + 6 = 0, is
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Given,
x|x| - 5|x + 2| + 6 = 0
Now taking case when x < - 2 we get,
-x 2 + 5x + 10 + 6 = 0
x 2 - 5x - 16 = 0
, ignoring 
as x < -2, so one solution is possible here,
Now taking case when -2 
x 
0 we get,
-x 2 - 5x - 10 + 6 = 0
x 2 + 5x + 4 = 0
, ignoring x = -4 as -2 
x < 0
Now taking case , when x 
0 we get,
x 2 - 5x - 10 + 6 = 0
x 2 – 5x - 4 = 0
ignoring 
as x 
0
So, from all cases we get total 3 solutions.
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