Question

Find a real number c such that x^(2)+12x+c is a perfect square trinomial.

Answer 1

Answer:

The value of c is 36

Step-by-step explanation:

Now, we fine the perfect square polynomial, we need to have the expression of the form:

$a^2+b^2+2ab$

so this can be written as a perfect square as: $a^2+b^2+2ab= (a+b)^2$

Now the expression given to us is:

$x^{2}+12x+c$

so when c is 36, we will get:

$x^{2}+12x+c= x^(2)+12x+36$

Now, this can be re-written as:

$x^{2}+2*6*x+6^2$

so here we can see that it is of the form:

$a^2+b^2+2ab$

so the perfect square is:

$x^(2)+2*6*x+6^2= (x+6)^2$

Hence, when c = 36 we get a perfect square.