What value of c makes x2+bx+c a perfect square trinomial?

For this case we have the following polynomial:

x2 + bx + c

To make the polynomial a perfect square, the value of c is:

c = (b / 2) ^ 2

Rewriting:

c = b ^ 2/2 ^ 2

c = b ^ 2/4

Substituting:

x2 + bx + b ^ 2/4

Where,

b is a constant.

Answer:

c = b ^ 2/4