Question

For what real values of $c$ is $x^2 - 8x + c$ the square of a binomial?

Answer 1

Value of c is 16 for which equation
`f(x) = x^2-8x+c` is a square of binomial !

Explanation:

Here we meed to find the value of c for which equation f(x) = x^2-8x+c or ,
`f(x) = x^2-8x+c` is a square of a binomial . Let's find out:

We know that

⇒
`(x-a)^2 = x^2-2(a)(x)+a^2` ..........(1)

Let's simplify given equation in question

⇒
`f(x) = x^2-8x+c`

⇒
`f(x) = x^2-2(4)x+c`

Comparing this equation with (1) we get :

`a=4 , c=a^2`

⇒
`c=a^2`

⇒
`c=4^2`

⇒
`c=16`

Therefore , Value of c is 16 for which equation
`f(x) = x^2-8x+c` is a square of binomial !