Question
Find the value of c that makes
x^2 + 12x + c a perfect square
trinomial.
𝖠 6
𝖡 9
𝖢 12
𝖣 36
x^2 + 12x + c a perfect square
trinomial.
𝖠 6
𝖡 9
𝖢 12
𝖣 36
Answers
Answered by
GPT-4o mini
To find 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 given by:
\[
(x + a)^2 = x^2 + 2ax + a^2
\]
From the expression \( x^2 + 12x + c \), we can see that:
- The coefficient of \( x \) is \( 12 \), which corresponds to \( 2a \).
Thus, we have:
\[
2a = 12 \implies a = \frac{12}{2} = 6
\]
Next, we need to find \( c \). A perfect square trinomial follows the form \( (x + a)^2 = x^2 + 2ax + a^2 \), and from our value of \( a \):
\[
a^2 = 6^2 = 36
\]
So, in order for \( x^2 + 12x + c \) to be a perfect square trinomial, \( c \) must equal \( 36 \).
Thus, the value of \( c \) that makes \( x^2 + 12x + c \) a perfect square trinomial is:
\[
\boxed{36}
\]
\[
(x + a)^2 = x^2 + 2ax + a^2
\]
From the expression \( x^2 + 12x + c \), we can see that:
- The coefficient of \( x \) is \( 12 \), which corresponds to \( 2a \).
Thus, we have:
\[
2a = 12 \implies a = \frac{12}{2} = 6
\]
Next, we need to find \( c \). A perfect square trinomial follows the form \( (x + a)^2 = x^2 + 2ax + a^2 \), and from our value of \( a \):
\[
a^2 = 6^2 = 36
\]
So, in order for \( x^2 + 12x + c \) to be a perfect square trinomial, \( c \) must equal \( 36 \).
Thus, the value of \( c \) that makes \( x^2 + 12x + c \) a perfect square trinomial is:
\[
\boxed{36}
\]
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