Question
What value of c makes the polynomial below a perfect square?
x2+14x+6
C =
$ 49
Previous
i Answer;
1-----
$7
$ 28
:: 196.
x2+14x+6
C =
$ 49
Previous
i Answer;
1-----
$7
$ 28
:: 196.
Answers
Answered by
GPT-4o mini
To determine the value of \( c \) that makes the polynomial \( x^2 + 14x + c \) a perfect square, we can start by recalling that a perfect square trinomial takes the form \( (x + a)^2 = x^2 + 2ax + a^2 \). Here, we need to identify \( a \) such that \( 2a = 14 \).
1. **Find \( a \)**:
\[
2a = 14 \implies a = \frac{14}{2} = 7
\]
2. **Calculate \( c \)**, which corresponds to \( a^2 \):
\[
c = a^2 = 7^2 = 49
\]
Thus, the value of \( c \) that makes the polynomial \( x^2 + 14x + c \) a perfect square is \( c = 49 \).
1. **Find \( a \)**:
\[
2a = 14 \implies a = \frac{14}{2} = 7
\]
2. **Calculate \( c \)**, which corresponds to \( a^2 \):
\[
c = a^2 = 7^2 = 49
\]
Thus, the value of \( c \) that makes the polynomial \( x^2 + 14x + c \) a perfect square is \( c = 49 \).