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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?

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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.

If the discriminant is equal to zero, then the quadratic equation has ___ solution(s).

Learn how to determine the number of solutions for a quadratic equation when the discriminant is zero. This concept explores the discriminant formula and provides insights into real and complex solutions. Perfect for students in Grades 7-9.

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