Answer
The third charge equals half of the magnitude of the other two charges
Work Step by Step
There are three charges, two of them have the same magnitude $q$ and the third is $q_o$. All of them far from each other with the same distance $r$. Also, we are given that the work is done or the potential energy for this system is zero.
So, the energy that assembles the three charges will be the summation of the potential energy of each charge and will be calculated in the form
\begin{gather*}
U = \dfrac{1}{4\pi \epsilon_o} \sum \dfrac{q q_i}{r_i}= 0\\
\dfrac{1}{4\pi \epsilon_o} \left( \dfrac{q^2}{r} + \dfrac{qq_o}{r}+ \dfrac{qq_o}{r}\right) = 0 \\
q^2 + qq_o+qq_o =0\\
q^2 + 2 qq_o = 0 \\
q+2q_o = 0\\
q_o = \dfrac{-q}{2}
\end{gather*}
Hence, the third charge equals half of the magnitude of the other two charges
