Question

What value of c makes the trinomial below a perfect square x2 + 5x + c

Answer 1

`c=(25)/(4)`

Explanation:

The given expression is

`x^2+5x+c` ...... (1)

If an expression is defined as
`x^2+bx`, then we need to add
`((b)/(2))^2` in it, to make it perfect square.

In the expression
`x^2+5x`, b=5.

`((b)/(2))^2=((5)/(2))^2=(25)/(4)`

Add
`(25)/(4)` in
`x^2+5x` to make it perfect square.

`x^2+5x+(25)/(4)` .... (2)

`x^2+5x+((5)/(2))^2`

`(x+(5)/(2))^2`
`[\because (a+b)^2=a^2+2ab+b^2]`

On comparing (1) and (2) we get

`c=(25)/(4)`

Therefore,
`x^2+5x+c` is a perfect square if
`c=(25)/(4)`.

Answer 2

Hello from MrBillDoesMath!

Answer:

25/4 = 6-1/4

Discussion:

Consider

(x+a)^2 = x^2 + (2a)x + a^2

The constant, a^2, needed to create a perfect square is (1/2) the coefficient of the x term squared. In our case, (1/2) 5 = 5/2 and the perfect square is

(x + 5/2)^2 =

x^2 + 2(5/2)x + (5/2)^2 =

x^2 + 5x + 25/4

As the question asks for the value of "c", the constant, the answer is 25/4,

Thank you,

MrB