Question

What value of c makes x2 − 12x + c a perfect square trinomial?

Answer 1

Answer:  The required value of c is 36.

Step-by-step explanation:  We are given to find the value of c so that the following expression becomes a perfect square trinomial :

$E=x^2-12x+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To find the value of c, we proceed as follows :

$E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times6+6^2)+c-6^2\\\\=(x-6)^2+c-36.$

So, for E to be a perfect square trinomial, we must have

$c-36=0\\\\\Righatrrow c=36.$

Thus, the required value of c is 36.

Answer 2

Answer:

for value 36

c makes the perfect square

x2 - 12x +36

= x2 - 2*6x +6^2

= (x-6)^2 #