Describe the 3 types of solution to a quadratic equation

The behaviour of the solution depends on the value of the discriminant, D = b² – 4ac, (aptly named as it allows you to discriminate between solutions)

If D > 0: The equation has real roots (the parabola will intersect the x axis twice)

If D = 0: The equation has a repeated real root (the vertex of the parabola lies on the x axis)

If D < 0: The equation has no real roots but rather 2 complex roots (the parabola does not intersect the x axis)