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. Skip to navigation

Question

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. Skip to navigation

GPT-4o mini · Answer

To determine whether the values $ x = -34 $, $ x = -12 $, and $ x = 12 $ are solutions to the quadratic equation $ -2x^2 - 3x + 2 = 0 $, we will substitute each value into the equation and check if the left side equals 0. 1. **For $ x = -34 $**: $$ -2(-34)^2 - 3(-34) + 2 $$ $$ = -2(1156) + 102 + 2 $$ $$ = -2312 + 102 + 2 $$ $$ = -2210 \quad (\text{not } 0) $$ 2. **For $ x = -12 $**: $$ -2(-12)^2 - 3(-12) + 2 $$ $$ = -2(144) + 36 + 2 $$ $$ = -288 + 36 + 2 $$ $$ = -250 \quad (\text{not } 0) $$ 3. **For $ x = 12 $**: $$ -2(12)^2 - 3(12) + 2 $$ $$ = -2(144) - 36 + 2 $$ $$ = -288 - 36 + 2 $$ $$ = -322 \quad (\text{not } 0) $$ Since none of the values yield 0, none of them are solutions to the equation. If you are looking for a value that makes the equation true (i.e., equal to 0), you might need to solve the equation $ -2x^2 - 3x + 2 = 0 $ using the quadratic formula or other methods. Since none of $ x = -34 $, $ x = -12 $, or $ x = 12 $ are solutions to the equation, the correct answer to your question is: Only $ x = $ none of the values are in the solution set.