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The number of real roots of |x|^3 – 3(x)^2 + 3|x| – 2 =0 is 1)1 2)2 3)3 4)none of these

The number of real roots of  |x|^3  – 3(x)^2  + 3|x| – 2 =0  is 
1)1
2)2
3)3
4)none of these

Grade:

1 Answers

Tony
13 Points
5 years ago
By differentiating ,equation becomes          3x^2-6x+3=3*(x-1)*(x-1).
So,at x =1, the above eq will be zero and hence it will be a turning point for the graph of the given equation.
As( x-1) is occurring twice ,it can be considered two turning points(actually one meet ing at same place on graph of the eq.mentinoned in the question.
So as their are 2 turning points , 
 
Number of real roots= turning points +1 
                                     =2+1=3
 
 
 

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