The problem asks to determine the number of solutions a quadratic equation has when its discriminant is zero.

1. Problem Description

The problem asks to determine the number of solutions a quadratic equation has when its discriminant is zero.

2. Solution Steps

The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

The discriminant is the term inside the square root: $b^2 - 4ac$.

If the discriminant is zero, then the quadratic formula becomes:

$x = \frac{-b \pm \sqrt{0}}{2a} = \frac{-b \pm 0}{2a} = \frac{-b}{2a}$.

Since the $\pm$ term vanishes when the discriminant is zero, there is only one solution for x. The quadratic equation will have one real solution.

3. Final Answer

one