To determine if -2 and 5 are solutions to the quadratic equation \( x^2 + 3x + 2 = 0 \), we can substitute each value into the equation and see if it holds true.
- Testing \( x = -2 \):
Substituting -2 into the equation gives:
\[ (-2)^2 + 3(-2) + 2 = 0 \]
Calculating each term:
\[ 4 - 6 + 2 = 0 \]
Combining these:
\[ 4 - 6 + 2 = 0 \implies 0 = 0 \]
This is true, so \( x = -2 \) is a solution.
- Testing \( x = 5 \):
Substituting 5 into the equation gives:
\[ (5)^2 + 3(5) + 2 = 0 \]
Calculating each term:
\[ 25 + 15 + 2 = 0 \]
Combining these:
\[ 25 + 15 + 2 = 42 \implies 42 \neq 0 \]
This is not true, so \( x = 5 \) is not a solution.
Final Answers:
- For \( x = -2 \): Yes, this is a solution.
- For \( x = 5 \): No, this is not a solution.