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.
To determine whether a given value is a solution to the quadratic equation, we need to substitute the value for x in the equation and evaluate whether the equation holds true.
Let's substitute the given values for x and evaluate the equation:
For x = -34:
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2208
For x = -12:
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250
For x = 12:
-2(12)^2 - 3(12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250
As we can see, none of the given values satisfy the quadratic equation -2x^2 - 3x + 2 = 0. Therefore, none of the values are in the solution set.