All solutions of the equation `4x^(2)-40x+51+40{x}=0` lies in the interval ( {•}represents fractional part )

One root of the equation cosx-x+1/2=0 lies in the interval

The smallest positive root of the equation tan x-x =0 lies in the interval

If x is real and 2x^(2)-4x+5>0, then x lies in the interval

The number of solution of the equation sgn({x})=|1-x| is/are (where {*} represent fractional part function and sgn represent signum function)

The number of solution of the equation sgn({x})=|1-x| is/are (where {*} represent fractional part function and sgn represent signum function)

The number of solutions of the equation x^(2)-3={x} ,where {x} is the fractional part of x is

The complete solution set of the equation sgn ((x^(2)-5x+4)/(x))=-1, where {*} is fractional part function is

Check the continuity of functions f(x)={x}^(2)-{x^(2)} at all integral points, where {.} represents fraction part.

Find the solution of the equation [x] + {-x} = 2x, (where [*] and {*} represents greatest integer function and fractional part function respectively.