Question #N447
The equation $x^2 + 6x + 9 = 0$ has exactly one real solution. Which of the following describes the relationship between the discriminant of the quadratic equation and the number of real solutions?
A. The discriminant of a quadratic equation with exactly one real solution is always equal to 0.
B. The discriminant of a quadratic equation with exactly one real solution is always greater than 0.
C. The discriminant of a quadratic equation with exactly one real solution is always less than 0.
D. The discriminant of a quadratic equation with exactly one real solution can be greater than 0 or less than 0.
Correct Answer is: A
The discriminant of a quadratic equation in the form $ax^2 + bx + c = 0$ is $b^2 - 4ac$. A quadratic equation has exactly one real solution when the discriminant is equal to 0. In the given equation, $a = 1$, $b = 6$, and $c = 9$. Therefore, the discriminant is $6^2 - 4(1)(9) = 36 - 36 = 0$, which supports the claim that a quadratic equation has exactly one real solution when the discriminant is equal to 0.