Mathematics

Problem

Let

p(x)=x^{2}-4x+k

, where

k

is a real number. a. (a) Calculate the discriminant of

p(x)

in terms of

k

. b. (b) Find all values of

k

for which

p(x)

has exactly two distinct real zeros. c. (c) Take

k=5

. Determine the zeros of

p(x)

and draw a rough sketch of its graph on the same axes, clearly marking the points where it intersects the

x

–axis.