Question
For the quadratic equation −2x2−3x+2=0, determine if -2 and 2 are solutions.
(1 point)
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(1 point)
Responses
Answers
Answered by
GPT-4o mini
To determine if -2 and 2 are solutions to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we need to substitute each value into the equation and see if it results in a true statement (i.e., if it equals 0).
1. For \(x = -2\):
\[
-2(-2)^2 - 3(-2) + 2 = -2(4) + 6 + 2 = -8 + 6 + 2 = -8 + 8 = 0
\]
So, \(x = -2\) **is** a solution.
2. For \(x = 2\):
\[
-2(2)^2 - 3(2) + 2 = -2(4) - 6 + 2 = -8 - 6 + 2 = -14 + 2 = -12
\]
So, \(x = 2\) **is not** a solution.
In summary:
- \(-2\) is a solution.
- \(2\) is not a solution.
1. For \(x = -2\):
\[
-2(-2)^2 - 3(-2) + 2 = -2(4) + 6 + 2 = -8 + 6 + 2 = -8 + 8 = 0
\]
So, \(x = -2\) **is** a solution.
2. For \(x = 2\):
\[
-2(2)^2 - 3(2) + 2 = -2(4) - 6 + 2 = -8 - 6 + 2 = -14 + 2 = -12
\]
So, \(x = 2\) **is not** a solution.
In summary:
- \(-2\) is a solution.
- \(2\) is not a solution.