Question

Determine whether the values -2 and 5 are solutions to the quadratic equation below.

x2+3x+2=0


(2 points)
Yes, this is a solution. No, this is not a solution.
x=−2


x=5

Answer 1

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.

1. **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.

2. **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.**