find the value of c that makes x^2+5x+c a perfect square trinomial?

Question

a. 25/16
b. 5/4
c. 25/4
d. 5/2

Answer 1

The answer is part c.: 25/4. Here's why:

(x + b)^2 = x^2 + 2 b x + b^2. Clearly, from the term in x, b = 5/2. Therefore:

c = b^2 = (5/2)^2 = 25/4. QED

Live long and prosper.

Answer 2

We want to find c so that x^2 + 5x + c can be written as (x + m)^2 for some number "m". If we multiply (x+m)^2 out, we get x^2 = 2mx + m^2. So to get this to match the original trinomial, we need 5 = 2m and c = m^2. This means m = 5/2, c must equal (5/2)^2 or 25/4. So the correct answer is "c".

Answer 3

To get a perfect square trinomial in that form,
you need 5 = 2(sqrt c)

so:

5 = 2(sqrt c)
5/2 = sqrt c
25/4 = c