Mathematics

Problem

Consider the quadratic polynomial

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

, where

k

is a real parameter. a. Find the condition on

k

for which the graph of the polynomial has exactly one

x

-intercept. b. Find the condition on

k

for which the graph has no

x

-intercepts. c. For a value of

k

that satisfies the condition in part (i), determine the

x

-coordinate of the single

x

-intercept.