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 each given value is a solution for the quadratic equation −2x^2−3x+2=0, we substitute each value into the equation and check if the equation holds true.
Given values: 1/2, 1, 2
Substituting 1/2 into the equation:
−2(1/2)^2−3(1/2)+2 = 0
−2(1/4)−3/2+2 = 0
-1/2 - 3/2 +2 = 0
-2 = 0 (not true)
Therefore, 1/2 is not a solution to the equation.
Substituting 1 into the equation:
−2(1)^2−3(1)+2 = 0
−2−3+2 = 0
-3 = 0 (not true)
Therefore, 1 is not a solution to the equation.
Substituting 2 into the equation:
−2(2)^2−3(2)+2 = 0
−2(4)-6+2 = 0
-8 - 6 +2 = 0
-12 +2 = 0
-10 = 0 (not true)
Therefore, 2 is not a solution to the equation.
None of the given values, 1/2, 1, or 2, are solutions to the quadratic equation −2x^2−3x+2=0.