Question

Determine whether the values -2 and 5 are solutions to the quadratic equation below. x^2 + 3x + 2 = 0

Answer 1

To determine if the values -2 and 5 are solutions to the quadratic equation \(x^2 + 3x + 2 = 0\), we will substitute each value into the equation and check if it results in a true statement (i.e., the equation equals 0).

1. **Substituting \(x = -2\)**:

\[
x^2 + 3x + 2 = 0
\]
\[
(-2)^2 + 3(-2) + 2 = 0
\]
\[
4 - 6 + 2 = 0
\]
\[
0 = 0 \quad \text{(True)}
\]

So, \(-2\) is a solution to the equation.

2. **Substituting \(x = 5\)**:

\[
x^2 + 3x + 2 = 0
\]
\[
(5)^2 + 3(5) + 2 = 0
\]
\[
25 + 15 + 2 = 0
\]
\[
42 \neq 0 \quad \text{(False)}
\]

So, \(5\) is not a solution to the equation.

**Conclusion:**
- The value \(-2\) is a solution to the equation \(x^2 + 3x + 2 = 0\).
- The value \(5\) is not a solution to the equation.