What does it mean if the discriminant is greater than 0?

When the discriminant of a quadratic equation is greater than 0, it indicates that the equation has two distinct real solutions. The discriminant is calculated from the quadratic formula, specifically as (b^2 - 4ac) for a quadratic equation in the form (ax^2 + bx + c = 0).

A positive discriminant implies that the expression under the square root in the quadratic formula (\sqrt{b^2 - 4ac}) is positive. This results in two different values when you perform the calculation, leading to two distinct points where the graph of the quadratic function intersects the x-axis. Thus, having two distinct real solutions means that the quadratic function has two different x-values at which it equals zero, contributing to the understanding that the parabola opens either upwards or downwards based on the leading coefficient (a).

Understanding the implications of the discriminant helps in analyzing the nature of the roots of quadratic equations, which is an essential concept in algebra and functions.