What does it mean when the discriminant in the quadratic formula is equal to 0?

When the discriminant in the quadratic formula is equal to 0, it indicates that the quadratic equation has exactly one real root. The discriminant is part of the quadratic formula, which is expressed as ( ax^2 + bx + c = 0 ). The value of the discriminant is calculated using the formula ( b^2 - 4ac ).

When the discriminant equals 0, this means that the expression ( b^2 - 4ac ) results in zero, suggesting that the quadratic touches the x-axis at a single point, or in other words, there is only one solution to the equation. This single root is also known as a repeated or double root.

In contrast, when the discriminant is positive, the quadratic has two distinct real roots, and when it is negative, the equation has no real solutions and instead has two complex roots. Thus, the scenario where the discriminant is zero is unique because it signifies a perfect square trinomial, leading to one real solution rather than multiple solutions.