If the discriminant in the quadratic formula is greater than 0, how many real roots exist?

In the context of quadratic equations, the discriminant is a key component of the quadratic formula, which is used to find the roots of a quadratic equation in the standard form ( ax^2 + bx + c = 0 ). The discriminant is given by the expression ( b^2 - 4ac ).

When the discriminant is greater than 0, it indicates that there are two distinct real roots for the quadratic equation. This means that the graph of the quadratic function intersects the x-axis at two different points. Each of these intersections represents a real solution to the equation.

If the discriminant were equal to 0, there would be exactly one real root, which is the case where the graph touches the x-axis at a single point (a repeated root). On the other hand, if the discriminant were less than 0, it would indicate that there are no real roots, as the graph of the function does not intersect the x-axis at all and instead represents complex roots.

Therefore, when the discriminant is greater than 0, the conclusion is that there are indeed two real roots, confirming that the correct understanding aligns with having two distinct values for ( x ) that satisfy the equation.