Mathematics

Problem

Consider the cubic polynomial

F(x)=kx^3+2x^2-5x+c,

where

k

and

c

are real constants. The graph of

F

passes through the points

(0,12)

and

(1,0)

. a. (i) Find the values of

c

and

k

. b. (ii) State the y-intercept of the graph of

F

in coordinate form once

c

and

k

have been determined. c. (iii) Verify that the point

(1,0)

lies on the curve with the values of

k

and

c

found in part (i).