Question
Solve for p.
p2+7p+12=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
p=
p2+7p+12=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
p=
Answers
GPT-4o mini
To solve the quadratic equation \( p^2 + 7p + 12 = 0 \), we can factor it.
First, we look for two numbers that multiply to \( 12 \) (the constant term) and add up to \( 7 \) (the coefficient of \( p \)).
The factors of \( 12 \) that sum to \( 7 \) are \( 3 \) and \( 4 \).
Thus, we can factor the equation as follows:
\[
(p + 3)(p + 4) = 0
\]
Now, we set each factor equal to zero:
1. \( p + 3 = 0 \) gives us \( p = -3 \)
2. \( p + 4 = 0 \) gives us \( p = -4 \)
The solutions are:
\[
p = -3, -4
\]
Therefore, the final answer is:
\[
p = -3, -4
\]
First, we look for two numbers that multiply to \( 12 \) (the constant term) and add up to \( 7 \) (the coefficient of \( p \)).
The factors of \( 12 \) that sum to \( 7 \) are \( 3 \) and \( 4 \).
Thus, we can factor the equation as follows:
\[
(p + 3)(p + 4) = 0
\]
Now, we set each factor equal to zero:
1. \( p + 3 = 0 \) gives us \( p = -3 \)
2. \( p + 4 = 0 \) gives us \( p = -4 \)
The solutions are:
\[
p = -3, -4
\]
Therefore, the final answer is:
\[
p = -3, -4
\]