In terms of real-number solutions, how many solutions can a quadratic equation have?

• A. Exactly 2
• B. Exactly 1
• C. 0, 1, or 2
• D. Infinitely many

Answer: (C)

Verified step by step guidance

1. Recall that a quadratic equation is generally written as \(ax^2 + bx + c = 0\), where \(a \neq 0\).
2. The number of real solutions depends on the discriminant, which is calculated as \(\Delta = b^2 - 4ac\).
3. If \(\Delta > 0\), the quadratic equation has exactly 2 distinct real solutions.
4. If \(\Delta = 0\), the quadratic equation has exactly 1 real solution (a repeated root).
5. If \(\Delta < 0\), the quadratic equation has no real solutions (the solutions are complex or imaginary). Therefore, the number of real solutions can be 0, 1, or 2.