Let `[x]` denote the greatest integer function. What is the number of solutions of the equation `x^2 - 4x + [x] = 0` in the interval `[0, 2]` ?

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. Let [x] denote the greatest integar function. What is the number of solutions of the equation x^(2) - 4x+ [x] - 0 " in the interval " [0,2] ?

If [x] denotes the greatest integer le x , then number of solutions of the equation x^(2) - 2 - 2 [x] =0 is

If [x] denotes the greatest integer function .Find the solution set of equation [x]^2 +5[x] +6=0

Let [x] denote the greatest integer in x .Then in the interval [0,3] the number of solutions of the equation,x^(2)-3x+[x]=0 is

If [x] denotes the greatest integer function and [e^x]^2+[e^x+1]-3=0 then x in