Question

Use the table to answer the 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. Skip to navigation

Answer 1

To determine whether the values \( x = -34 \), \( x = -12 \), and \( x = 12 \) are solutions to the quadratic equation \( -2x^2 - 3x + 2 = 0 \), we will substitute each value into the equation and check if the left side equals 0.

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

Since none of the values yield 0, none of them are solutions to the equation.

If you are looking for a value that makes the equation true (i.e., equal to 0), you might need to solve the equation \( -2x^2 - 3x + 2 = 0 \) using the quadratic formula or other methods.

Since none of \( x = -34 \), \( x = -12 \), or \( x = 12 \) are solutions to the equation, the correct answer to your question is:

Only \( x = \) none of the values are in the solution set.