Final answer:
A quadratic equation with a discriminant of -36 has two complex roots since the discriminant is negative. These roots are conjugate pairs and cannot be represented as points where the graph intersects the x-axis on a two-dimensional graph.
Step-by-step explanation:
When a quadratic equation with real coefficients has a discriminant of -36, it means that the equation does not have real roots. The discriminant, which is calculated as the part of the quadratic formula b² - 4ac, determines the nature of the roots of a quadratic equation. If the discriminant is negative, as in this case, the quadratic equation will have two complex roots. These complex roots are conjugates of each other and can be found using the quadratic formula: -b ± √(b² - 4ac) over 2a. In a two-dimensional (x-y) graph, this equation will not intersect the x-axis, as its solutions are not real numbers.