Case 1: Parabola crosses the x-axis twice → we obtain two intersections, 2 solutions Case 2: Parabola crosses the x-axis once → we obtain one intersection, 1 solution

Case 3: Parabola does not cross the x-axis → we obtain zero intersections, no (real) solution

Question: discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Think of an example, where you take the standard form of a quadratic equation and use the quadratic formula to find the solutions (if any). Indicate which case your example falls into (one of three cases listed above).