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.