The solutions of the quadratic equation Ax^2+Bx+C=0 are called roots and are given by a famous equation called the Quadratic Formula . In the quadratic formula, the terms B^2-4AC underneath the radical have a special name: the Discriminant .

Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.