Question

1. Use the table to complete the statement.

x Substituted Evaluate True Statement?
−34

−12

12



(1 point)
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. Only x =

is in the solution set.

Answer 1

To determine which values from the table are solutions to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we need to substitute each value of \(x\) into the equation and evaluate whether the equation holds true (i.e., if it equals zero).

Let's evaluate each of the values:

1. **For \(x = -34\):**

\[
-2(-34)^2 - 3(-34) + 2
\]
\[
= -2(1156) + 102 + 2
\]
\[
= -2312 + 102 + 2
\]
\[
= -2312 + 104 = -2208 \quad (\text{False Statement})
\]

2. **For \(x = -12\):**

\[
-2(-12)^2 - 3(-12) + 2
\]
\[
= -2(144) + 36 + 2
\]
\[
= -288 + 36 + 2
\]
\[
= -288 + 38 = -250 \quad (\text{False Statement})
\]

3. **For \(x = 12\):**

\[
-2(12)^2 - 3(12) + 2
\]
\[
= -2(144) - 36 + 2
\]
\[
= -288 - 36 + 2
\]
\[
= -288 - 34 = -322 \quad (\text{False Statement})
\]

Based on our calculations, none of the values yield a true statement where the equation equals zero. Thus, it seems that no values from the table are in the solution set.

Hence, you can complete the statement as follows:

Only \(x = \textbf{None}\) is in the solution set.