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.
To determine whether a given value is a solution to the quadratic equation -2x^2 - 3x + 2 = 0, we substitute the value into the equation and check if the equation holds true.
Given values to test: -2, -1, 1, 2
Substituting -2 into the equation:
-2(-2)^2 - 3(-2) + 2 = -2(4) + 6 + 2 = -8 + 6 + 2 = 0
Since the equation equals 0, -2 is a solution.
Substituting -1 into the equation:
-2(-1)^2 - 3(-1) + 2 = -2(1) + 3 + 2 = -2 + 3 + 2 = 3
Since the equation does not equal 0, -1 is not a solution.
Substituting 1 into the equation:
-2(1)^2 - 3(1) + 2 = -2(1) - 3 + 2 = -2 - 3 + 2 = -3
Since the equation does not equal 0, 1 is not a solution.
Substituting 2 into the equation:
-2(2)^2 - 3(2) + 2 = -2(4) - 6 + 2 = -8 - 6 + 2 = -12
Since the equation does not equal 0, 2 is not a solution.
Therefore, the solution set for the quadratic equation -2x^2 - 3x + 2 = 0 is {-2}.