Understanding Quadratic Equations | The Significance of a Discriminant of Zero

If b²-4ac = 0

If b²-4ac = 0, then it means that the discriminant of a quadratic equation is zero

If b²-4ac = 0, then it means that the discriminant of a quadratic equation is zero. The discriminant is the expression found under the square root when solving a quadratic equation in the form ax² + bx + c = 0.

In general, the discriminant is given by the formula b²-4ac. It is used to determine the nature of the solutions (roots) of a quadratic equation. When the discriminant is zero, it indicates that the quadratic equation has exactly one real root or, in other words, it has a repeated root.

To understand this concept more clearly, let’s consider an example of a quadratic equation:

2x² + 5x + 2 = 0

In this case, a = 2, b = 5, and c = 2. We can calculate the discriminant as:

b²-4ac = (5)² – 4(2)(2) = 25 – 16 = 9

Since the discriminant is positive (9 > 0), the quadratic equation has two distinct real roots. However, if the discriminant is zero as in your question, it would look like this:

b²-4ac = 0

This means that the quadratic equation has exactly one real root, which is repeated. In visually representing this quadratic equation on a graph, its graph would touch the x-axis at a single point.

To solve the quadratic equation when the discriminant is zero, we can use the quadratic formula:

x = (-b ± √(b² – 4ac)) / (2a)

Since the discriminant is zero, we have:

x = (-b ± √0) / (2a)

Simplifying further, we get:

x = -b / (2a)

Therefore, when the discriminant is zero, the quadratic equation has only one real root given by -b / (2a).

More Answers: