Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The number of roots of the equation 
, is
Text Solution
Verified by ExpertsThe correct answer is:
B
Given 
where [ ] denotes the greatest integer function.
Domain 
since 
is defined only on 
.
Also, 
is the fractional part 
, so
Hence 
must be 0 or 1 .
Case analysis
Case 1: 
For 
, so RHS 
.
Thus 
Giving 
Case 2: 
For 
except at 
.
Equation becomes 
Giving 
Check: 
and 
So 
is not a solution.
Hence only 
satisfies the equation.
Number of roots = 1
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