Mathematics

Problem

Let

P(x) = (k + 1)x + (3 - 2k)

, where

k

is a real number. a. (i) Determine the value of

k

for which

x = 4

is the zero of

P(x)

. b. (ii) Using this value of

k

, write the equation of the line

y = P(x)

and find its

y

-intercept. c. (iii) Confirm algebraically that the point

(4, 0)

lies on the line obtained in part (ii).