Question

For the quadratic equation −2x2−3x+2=0
, determine if -2 and 2 are solutions.

(1 point)
Responses

Both x=−2
and x=2
are solutions.
Both x is equal to negative 2 and x is equal to 2 are solutions.

Only x=−2
is a solution.
Only x is equal to negative 2 is a solution.

Neither x=−2
nor x=2
is a solution.
Neither x is equal to negative 2 nor x is equal to 2 is a solution.

Only x=2
is a solution.
Only x is equal to 2 is a solution.
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Answer 1

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

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

\[
-2(-2)^2 - 3(-2) + 2
\]

Calculating each term:

\[
= -2(4) + 6 + 2
\]

\[
= -8 + 6 + 2
\]

\[
= -8 + 8
\]

\[
= 0
\]

So, \(x = -2\) is a solution.

2. **Testing \(x = 2\)**:

\[
-2(2)^2 - 3(2) + 2
\]

Calculating each term:

\[
= -2(4) - 6 + 2
\]

\[
= -8 - 6 + 2
\]

\[
= -8 - 4
\]

\[
= -12
\]

Since this does not equal zero, \(x = 2\) is not a solution.

Thus, the correct response is:

**Only \(x = -2\) is a solution.**