Answer
Additional forces are neccesary.
Work Step by Step
If we select an arbitrary axis of rotation that passes through the center of the rod, then both forces $F_1$ and $F_2$ will pass through the axis, so they produce no torques.
As a result, only force $F_3$ produces torque, which has no other torques to be balanced. Therefore, the rod cannot be in equilibrium. Additional forces are needed.
