Question

What value of c makes x2 − 12x + c a perfect square trinomial? −36 −24 24 36

Answer 1

Take half of the middle coefficient.
Then square it.

-12/2 = -6

(-6)^2 = 36

c = 36

Answer 2

Answer: The value of c must be 36 to make it perfect square trinomial.

Explanation:

A standard perfect square trinomial is $x^2+2ax+a^2=(x+a)^2$ where $a^2$ is the constant term.

Given trinomial $x^2-12x+c=x^2+2(-6)a+c$

On comparing with standard perfect square trinomial we get a=-6

Therefore the constant term c=$a^2=(-6)^2=36$

Such that the trinomial becomes $x^2-12x+36=x^2+2(-6)x+(-6)^2=(x-6)^2$ a perfect square trinomial.

Hence the value of c for the given trinomial must be 36 to make it perfect square trinomial.