Which statement about discriminant values is true?

Which statement about discriminant values is true?

• A. There are no real solutions.
• B. There are two real solutions.
• C. There is exactly one real solution.
• D. There are infinitely many solutions.

Answer: (B)

The key idea is how the discriminant decides how many real roots a quadratic has. For a quadratic equation, the discriminant is b^2 − 4ac. If this value is positive, you get two distinct real solutions. If it’s zero, you get exactly one real solution (a double root). If it’s negative, there are no real solutions (the roots are complex). So the statement that there are two real solutions corresponds to the case where the discriminant is positive, which is why that option is correct. The other choices describe the other possible outcomes: zero real solutions for a negative discriminant, exactly one real solution for a zero discriminant, and infinite solutions don’t occur for a standard quadratic over the real numbers.

The key idea is how the discriminant decides how many real roots a quadratic has. For a quadratic equation, the discriminant is b^2 − 4ac. If this value is positive, you get two distinct real solutions. If it’s zero, you get exactly one real solution (a double root). If it’s negative, there are no real solutions (the roots are complex). So the statement that there are two real solutions corresponds to the case where the discriminant is positive, which is why that option is correct. The other choices describe the other possible outcomes: zero real solutions for a negative discriminant, exactly one real solution for a zero discriminant, and infinite solutions don’t occur for a standard quadratic over the real numbers.