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If a belong to R and equation -3(x-[x])^2+2(x-[x])+a^2 =0 has a no integral solution then find all possible values of a

If a belong to R and equation -3(x-[x])^2+2(x-[x])+a^2 =0 has a no integral solution then find all possible values of a
 

Grade:12th pass

1 Answers

Abhishek Singh
105 Points
one year ago
Clearly x-[x] = {x} where {x} is the fractional part function. Now the given equation is quadratic in {x}
-3{x}^2+2{x}+a^2 = 0 
 
We know that if {x} = 0 ==> x is an integer 
Thus the solution has integer solution if {x}= 0 satifies the equation  ==> if -3*0^2+2*0+a^2 = 0 ==> if a= 0 
But it is given equation has no integral solution ==> a is not equal to zero 

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