Solution:
1. Given:
- A real number x such that x^2 = 0.
2. Solve for x:
- Since x^2 = 0 implies that x \cdot x = 0, the only real number that satisfies this equation is x = 0.
- Therefore, the set A consists only of the number zero.
3. Conclusion:
- The set A can be represented as A = \{0\}.