Question

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

Answer 1

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

Answer 2

Answer:

$c=\frac{25}{4}$

Step-by-step explanation:

The given expression is

$x^2+5x+c$                ...... (1)

If an expression is defined as $x^2+bx$, then we need to add $(\frac{b}{2})^2$ in it, to make it perfect square.

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

$(\frac{b}{2})^2=(\frac{5}{2})^2=\frac{25}{4}$

Add $\frac{25}{4}$ in $x^2+5x$ to make it perfect square.

$x^2+5x+\frac{25}{4}$      .... (2)

$x^2+5x+(\frac{5}{2})^2$

$(x+\frac{5}{2})^2$                $[\because (a+b)^2=a^2+2ab+b^2]$

On comparing (1) and (2) we get

$c=\frac{25}{4}$

Therefore, $x^2+5x+c$ is a perfect square if $c=\frac{25}{4}$.