The problem states: "If the discriminant in the quadratic formula is zero, then the quadratic equation will have ______ solution(s)." We need to determine the number of solutions when the discriminant of a quadratic equation is zero.

1. Problem Description

The problem states: "If the discriminant in the quadratic formula is zero, then the quadratic equation will have ______ solution(s)." We need to determine the number of solutions when the discriminant of a quadratic equation 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 under the square root:

$D = b^2 - 4ac$

If $D > 0$, the quadratic equation has two distinct real solutions.

If $D = 0$, the quadratic equation has one real solution (or two equal real solutions).

If $D < 0$, the quadratic equation has no real solutions (two complex solutions).

Since the problem states that the discriminant is zero ($D = 0$), the quadratic equation has one real solution.

The quadratic formula then simplifies to:

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

3. Final Answer

One