Final answer:
The real solutions of ax² + bx + c = 0 are the x-intercepts of the quadratic function's graph, found using the quadratic formula.
Step-by-step explanation:
The real solutions of ax² + bx + c = 0 correspond to the x-intercepts of the graph of y = ax² + bx + c. In the context of a quadratic equation, the real solutions refer to the points where the parabola (the graph of the quadratic function) crosses the x-axis. These solutions are found using the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
For an equation to have real solutions, the discriminant (the part of the quadratic formula under the square root, b²-4ac) must be greater than or equal to zero. If the discriminant is zero, there is exactly one real solution, and if it is positive, there are two distinct real solutions. These solutions also indicate how many times the parabola touches or intersects the x-axis.