Answer
The third particle should be positively charged.
Work Step by Step
As we found in part (a), a third particle should be placed between these two particles.
The force on the $-q$ charge due to the $-3q$ charge is directed to the right. If the third particle is positively charged, the force on the $-q$ charge due to the third particle will be directed to the left. Then the $-q$ charge can be in equilibrium if the net force is zero.
A similar argument holds for the $-3q$ particle.
The third particle should be positively charged.
