Final answer:
The electric field is zero at x = 0.0 cm and at infinity. The electric potential can be zero at any position on the x-axis where the potential due to the positive and negative charges cancel out, such as x = 0.0 cm.
Step-by-step explanation:
The electric field is the force experienced by a unit charge at a particular point. To find the position(s) on the x-axis where the electric field is zero, we need to consider the charges and their positions. Since the charges are symmetrically placed at x = -1.0 cm and x = +1.0 cm, there will be two positions where the electric field is zero. One position is in between the charges, at x = 0.0 cm. At this point, the field due to the positive charge cancels out the field due to the negative charge. The other position is at infinity, where the field due to both charges approaches zero.
The electric potential, on the other hand, represents the amount of work done to bring a unit positive charge from infinity to a specific point. The electric potential can be zero at any position on the x-axis as long as the values of the electric potentials due to the two charges cancel each other out. This happens at x = 0.0 cm, where the positive and negative charges have equal magnitudes.