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

1 answer

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.

  1. 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.