The question here relates to the number of solutions of a quadratic equation based on the discriminant, which is derived from the quadratic formula $ax^2 + bx + c = 0$. The discriminant is given by $D = b^2 - 4ac$.

To determine the number of solutions:

• If $D > 0$, there are two distinct real solutions.
• If $D = 0$, there is one real solution (also called a repeated or double root).
• If $D < 0$, there are no real solutions (instead, there are two complex solutions).

Since the question specifies that the discriminant is equal to zero ($D = 0$), this corresponds to one real solution.

Thus, the correct answer for this question is:

• 1 solution.

Would you like a more detailed explanation of how the discriminant works, or do you have further questions?

Here are 5 related questions that build on this information:

1. What are the solutions if the discriminant is positive?
2. How do complex solutions arise in a quadratic equation?
3. What role does the discriminant play in determining the nature of roots?
4. How can the quadratic formula be derived?
5. Can a quadratic equation have infinitely many solutions?

Tip: Remember, the discriminant $b^2 - 4ac$ not only determines the number of solutions but also provides insights into whether the solutions are real or complex.