Answer
No value of q makes the Force on each of the four particles zero
Work Step by Step
The net force on particle 2 would be $\frac{Q}{q}=- \frac{1}{2\sqrt 2}$
This would be the same result for force on particle 3.
Due to this, there is no value of q that can make the net force on particle 1,2,3,4 equal to zero because of their distinct ratio.
