Consider the three quadratic polynomials
(a) p(x)=2x2−3x+5,
(b) q(x)=x2−4x+4,
(c) r(x)=3x2+5x−2.
Answer the following questions.
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.