The number of solutions of the equation x2+[x]−4x+3=0 is (where [ ] denotes G.I.F.)
0
Given equation can be written as (x2−3x+3)−f=0 where f=x−[x] and 0≤f<1
∴ 0 ≤x2−3x+3<1
Now, solving x2−3x+3=0 we get imaginary roots.
∴ x2−3x+3≥0 ∀ x∈R
Solving x2−3x+3<1 ⇒1<x<2
If 1<x<2;[x]=1 putting [x]=1 in the given equation and solving we get x=2. But 1<x<2
∴ The given equation has no solution.