Hint: Use the Coulomb's law.

Explanation: The net force on $q_1$ by $q_2$ and $q _3$ is along the $+x\text-$direction, so the nature of force between $q_1, q_2$ and $q_1, q_3$ is attractive. This can be represented by the figure given below.
 The attractive force between these charges states that $q_1$ is a negative charge (since $q_2$ and $q _3$ are positive).
Thus, the nature of force between $q_1$ and newly introduced charge $Q$ (positive) is also attractive and the net force on $q_1$ by $q_2,$ $q _3$ and $Q$ are along the same direction as given in the diagram below.

The figure given above clearly shows that the force on $q_1$ shall increase along the positive $x\text -$axis due to the positive charge $Q.$ Since positive charge $q_2$ and $q _3$ exert a net force in the $x\text -$direction on the charge $q_1$ fixed along the $x\text -$axis, the charge $q_1$ is negative as shown in the figure. Obviously, due to the addition of a positive charge $Q$ at $( x, 0 ),$ the force on $q_1$ shall increase along the positive $x\text -$axis.
Hence, option (1) is the correct answer.