Mathematics

Problem

A quadratic polynomial is given by

q(x)=x^{2}+ax+b

. It is known that

x=1

and

x=-2

are its zeros. a. (i) Form two separate equations in

a

and

b

using the given zeros. b. (ii) Solve the simultaneous equations to obtain the values of

a

and

b

. c. (iii) Write

q(x)

in its expanded standard form and verify that both given numbers are indeed its zeros.