Question

x Substituted Evaluate True Statement?
−34
−12
12
​For the quadratic equation −2x2−3x+2=0 , complete the table by testing each of the given values to determine whether it is a solution. Identify which one of the values is in the solution set.​

(1 point)
Only x=
is in the solution set.
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Answer 1

To determine which value is in the solution set of the quadratic equation \(-2x^2 - 3x + 2 = 0\), we will substitute each given \(x\) value into the equation and evaluate it. If the result equals zero, then that \(x\) value is a solution to the equation.

Let's evaluate each given value:

1. **For \(x = -34\):**
\[
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2210 \quad (\text{Not a solution})
\]

2. **For \(x = -12\):**
\[
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250 \quad (\text{Not a solution})
\]

3. **For \(x = 12\):**
\[
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322 \quad (\text{Not a solution})
\]

After evaluating each value:

- None of the values \(-34\), \(-12\), or \(12\) satisfy the equation \(-2x^2 - 3x + 2 = 0\) as they do not yield a true statement (i.e., they do not equal zero).

Thus, **none of the values is in the solution set** for the equation provided.