The force on a particle of mass m placed on smooth horizontal surface is $F=\left(2x^2-4\right)\mathrm{N}$ directed along positive X-axis. The particle is projected with minimum speed from $x=2 \mathrm{m}$ towards mean position along X-axis for crossing the origin, then the kinetic energy at 

If $F=0,x=\sqrt{2} \mathrm{m}$

When $x>\sqrt{2} \mathrm{m}$, force is directed away from the origin.

When $0\le x<\sqrt{2} \mathrm{m}$, force is directed towards origin. If the particle just cross$x=\sqrt{2} \mathrm{m}$, then it starts to accelerate. For minimum value of initial speed, the speed of particle should be zero at$x=\sqrt{2} \mathrm{m}$. This means that KE at $x=\sqrt{2}$ must be zero and it is non-zero at origin.