Question

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

Answer 1

To determine whether -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 we get a true statement (i.e., whether the left-hand side equals zero).

1. **Testing x = -2:**

Substitute -2 into the equation:
\[
(-2)^2 + 3(-2) + 2
\]
\[
= 4 - 6 + 2
\]
\[
= 4 - 6 + 2 = 0
\]

Since the left-hand side equals 0, \( x = -2 \) is a solution to the equation.

2. **Testing x = 5:**

Substitute 5 into the equation:
\[
(5)^2 + 3(5) + 2
\]
\[
= 25 + 15 + 2
\]
\[
= 25 + 15 + 2 = 42
\]

Since the left-hand side does not equal 0 (it equals 42), \( x = 5 \) is **not** a solution to the equation.

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