If [x2]+x−a=0 has a solution ([.] represents the greatest integer function), where a∈N,a≤20, then the total number of distinct values of a is
A
2
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B
3
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C
4
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D
6
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Solution
The correct option is C4 [x2]+x−a=0 ⇒[x2]−a=−x L.H.S. is an integer. So, x has to be an integer. ∴a=x2+x ⇒a=x(x+1) As a≤20, ∴a=2,6,12,20atx=1,2,3,4 respectively.