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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.

1 answer

To determine which values of \( x \) are solutions to the quadratic equation \( -2x^2 - 3x + 2 = 0 \), we will substitute each value of \( x \) from the table into the equation and check if the equation evaluates to \( 0 \).

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

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

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

After testing all values, none of them evaluate to \( 0 \). Thus, according to the solutions we have checked:

Only \( x = \text{none} \) is in the solution set (meaning none of the given values satisfy the equation).

So the answer is: Only \( x = \) none is in the solution set.