Question

Which of the following values completes the square or creates a perfect square trinomial for x^2-12x+___

-6
12
36
-36

Answer 1

Answer: The correct option is

(C) 36.

Step-by-step explanation: We are given to select the value that completes the square or creates a perfect square trinomial for the following incomplete expression :

`E=x^2-12x+?`

We will be using the following square formula :

`a^2-2ab+b^2=(a-b)^2.`

Let the required value be represented by c.

We have

`E\\\\=x^2-12x+c\\\\=(x^2-2* x* 6+6^2)+c-6^2\\\\=(x-6)^2+c-36.`

So, for the given expression to be a perfect square trinomial, we must have

`c-36=0\\\\\Rightarrow c=36.`

Thus, the required value is 36.

Option (C) is CORRECT.

Answer 2

So, 36 completes perfect square

Explanation:

we are given

trinomial as

`x^2-12x+......`

we can square formula

`a^2-2ab+b^2=(a-b)`

we can see that middle term is 2ab

so, we will factor middle term in 2ab form

`12x=2* x* 6`

We can see that b is 6

so, if we could add 6^2 , then we will get perfect square

`x^2-12x+6^2......`

`x^2-12x+36......`

So, we should add 36

so, 36......Answer