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.
To determine if a given value is a solution to the quadratic equation −2x^2 − 3x + 2 = 0, we substitute it in for x and evaluate the equation.
For x = −34:
−2(−34)^2 − 3(−34) + 2 = −2(1156) + 102 + 2 = −2312 + 102 + 2 = −2208 + 2 = −2206
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
None of the given values result in the equation being true. Therefore, none of the values are in the solution set. The statement "Only x= is in the solution set" is incorrect.
To determine whether a given value is a solution to a quadratic equation, you need to substitute the value into the equation and evaluate if the resulting statement is true.
Given the equation -2x^2 - 3x + 2 = 0, we can test each of the given values (-34, -12, 12) to determine if it satisfies the equation.
Substituting -34 into the equation:
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2208 + 2 = -2206
Since -2206 is not equal to 0, the statement is false.
Substituting -12 into the equation:
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250
Since -250 is not equal to 0, the statement is false.
Substituting 12 into the equation:
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322
Since -322 is not equal to 0, the statement is false.
Based on the table, none of the given values satisfy the equation, therefore, none of them are in the solution set.
To determine whether each given value is a solution to the quadratic equation -2x^2 - 3x + 2 = 0, we substitute each value into the equation and check if the result is true.
Substituting x = -34:
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2208
Since -2208 is not equal to 0, x = -34 is not a solution.
Substituting x = -12:
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250
Since -250 is not equal to 0, x = -12 is not a solution.
Substituting x = 12:
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322
Since -322 is not equal to 0, x = 12 is not a solution.
Based on the given table, none of the values (-34, -12, and 12) are in the solution set of the quadratic equation -2x^2 - 3x + 2 = 0. Therefore, the statement 'Only x= is in the solution set' is incorrect.