Mathematics

Problem

Answer the following questions related to perfect square trinomials of the form

x^2+bx+c

. a. (i) Define a perfect square trinomial having leading coefficient

1

. b. (ii) Verify that the polynomial

x^2+10x+25

is a perfect square trinomial. c. (iii) Factorise

x^2+10x+25

and hence write the general condition connecting

b

and

c

for which the trinomial

x^2+bx+c

becomes a perfect square.