Answer
The equilibrium is an unstable equilibrium.
Work Step by Step
In part (a) and part (b), we found that a positively charged third particle should be placed between the two given particles in order to achieve equilibrium.
If the third particle is placed in a specific location, the magnitude of the forces on the third particle due to the other two particles will be equal in magnitude and opposite in direction.
Let's suppose the location of the third particle is slightly to the left of the equilibrium position. Then the force directed to the left due to the $-3q$ particle will be greater in magnitude than the force directed to the right due to the $-q$ particle. In this case, the third particle will have a net force to the left, and continue moving more to the left. The third particle will not return to the equilibrium position.
A similar argument holds if the third particle is place placed slightly to the right of the equilibrium position.
Therefore, the equilibrium is an unstable equilibrium.
