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The solutions (aka roots) of a quadratic equation can be seen on the graph of the equation, which is a parabola, at the two point of intersection of the parabola with the x-axis.
Now you really have three situations depending on just where the parabola is located on the graph (coordinate grid).
1) The parabola does not intersect the x-axis at all. In this case, there are no real roots, the two roots or solutions will be complex conjugates (red graph).
2) The vertex of the parabola just touches the x-axis. In this case there will be one real root, also called a double root (green graph).
3) The parabola intersects the x-axis in two places. In this case, there will be two real roots (blue graph).