Mathematics

Problem

Let

P(x)=ax^{2}+bx+c

be a quadratic polynomial. It is given that

P(2)=0

P(-3)=0

, and

P(1)=4

. a. (i) Form a system of three equations in

a

b

, and

c

using the information provided. b. (ii) Solve the system to determine the values of

a

b

, and

c

. c. (iii) Write the quadratic polynomial

P(x)

in its expanded form and confirm that it satisfies all the given conditions.