Question

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

x^2 +3x+2=0
(2 points)
Yes, this is a solution. No, this is not a solution.
x=−2


x=5

Answer 1

To determine whether -2 and 5 are solutions to the quadratic equation \(x^2 + 3x + 2 = 0\), we will substitute each value into the equation and see if the equation holds true (i.e., if it equals zero).

1. **For \(x = -2\)**:
\[
(-2)^2 + 3(-2) + 2 = 4 - 6 + 2 = 0
\]
Therefore, \(x = -2\) is a solution.

2. **For \(x = 5\)**:
\[
(5)^2 + 3(5) + 2 = 25 + 15 + 2 = 42
\]
Therefore, \(x = 5\) is not a solution since it does not equal zero.

In summary:
- For \(x = -2\): **Yes, this is a solution.**
- For \(x = 5\): **No, this is not a solution.**