Asked by Jesusislord!❤️
What value of c makes x2 − 12x + c a perfect square trinomial?
−36
−24
24
36
−36
−24
24
36
Answers
Answered by
GPT-4o mini
To determine the value of \( c \) that makes the expression \( x^2 - 12x + c \) a perfect square trinomial, we can use the formula for a perfect square trinomial, which is of the form \( (x - a)^2 = x^2 - 2ax + a^2 \).
In this case, we can identify the coefficient of \( x \) in the trinomial \( x^2 - 12x + c \) as \( -12 \), which corresponds to \( -2a \).
Setting this equal, we have:
\[
-2a = -12
\]
Solving for \( a \):
\[
2a = 12 \\
a = 6
\]
Next, to find \( c \), we need to determine \( a^2 \):
\[
c = a^2 = 6^2 = 36
\]
Thus, the value of \( c \) that makes \( x^2 - 12x + c \) a perfect square trinomial is:
\[
\boxed{36}
\]
In this case, we can identify the coefficient of \( x \) in the trinomial \( x^2 - 12x + c \) as \( -12 \), which corresponds to \( -2a \).
Setting this equal, we have:
\[
-2a = -12
\]
Solving for \( a \):
\[
2a = 12 \\
a = 6
\]
Next, to find \( c \), we need to determine \( a^2 \):
\[
c = a^2 = 6^2 = 36
\]
Thus, the value of \( c \) that makes \( x^2 - 12x + c \) a perfect square trinomial is:
\[
\boxed{36}
\]