Question

Use the table to answer the question.

x Substituted Evaluate True Statement?
−34
−12
12
​For the quadratic equation −2x^2−3x+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.

Answer 1

To determine which of the values given in the table is a solution to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we will substitute each value of \(x\) into the equation and evaluate it.

1. For \(x = -34\):
\[
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2210 \quad (\text{not } 0)
\]

2. For \(x = -12\):
\[
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250 \quad (\text{not } 0)
\]

3. For \(x = 12\):
\[
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322 \quad (\text{not } 0)
\]

None of the given values make the equation equal to zero. Therefore, none of the values \(-34\), \(-12\), or \(12\) are solutions to the equation \(-2x^2 - 3x + 2 = 0\).

Thus, the answer to the question is:
Only \(x = \) (none) is in the solution set.