Consider the three quadratic polynomials
(a) Define the discriminant of a quadratic polynomial of the form ax2+bx+c.
(b) Explain the relation between the sign of the discriminant and the manner in which the graph of the quadratic polynomial meets the x-axis.
(c) For each of the polynomials (a), (b) and (c), determine whether its graph cuts the x-axis at two distinct points, touches it at exactly one point, or does not meet it at all. Give reasons for each answer.