Understanding Quadratic Equations | The Significance of b²-4ac > 0

If b²-4ac > 0

The inequality b²-4ac > 0 is related to the discriminant of a quadratic equation, which is determined by the coefficients a, b, and c

The inequality b²-4ac > 0 is related to the discriminant of a quadratic equation, which is determined by the coefficients a, b, and c. The discriminant is used to understand the nature of the solutions of a quadratic equation.

In this case, if b²-4ac > 0, it means that the discriminant is positive. Let’s break down the implications of this:

1. Two real and distinct solutions: When the discriminant is positive, it indicates that the quadratic equation has two distinct real solutions. The equation crosses the x-axis at two different points, meaning there are two different values of x that satisfy the equation.

2. Graphical interpretation: If you were to graph the quadratic equation, the parabola would intersect the x-axis at two distinct points. The graph may open upwards (if a > 0) or downwards (if a < 0), depending on the leading coefficient. 3. Relationship to the quadratic formula: The quadratic formula is used to find the solutions of a quadratic equation. When the discriminant is positive, the quadratic formula will give two real and distinct solutions. The formula is: x = (-b ± √(b²-4ac))/(2a), where the ± indicates that there will be two solutions - one with the positive square root and one with the negative square root. It is important to note that when b²-4ac > 0, it does not specify the values of a, b, and c. It simply indicates a characteristic of the solutions to the quadratic equation. Other cases where the discriminant can lead to different outcomes include when the discriminant is equal to zero (b²-4ac = 0) or when it is negative (b²-4ac < 0). Remember to always consider the context and any specific instructions or constraints provided when applying this inequality.

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