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 whether a given value is a solution to the quadratic equation, we need to substitute the value into the equation and evaluate whether the equation is true or false. Let's follow the given instructions and complete the table by testing each of the given values.
For the given quadratic equation −2x^2−3x+2=0, we need to substitute the values -34, -12, and 12 into the equation and evaluate whether the equation is true or false.
Let's start with the first value, x = -34:
Substituting x = -34 into the equation, we have:
-2(-34)^2 - 3(-34) + 2 = 0
Simplifying this, we get:
-2(1156) + 102 + 2 = 0
-2312 + 102 + 2 = 0
-2308 + 2 = 0
-2306 = 0
Since -2306 does not equal 0, the equation is false for x = -34.
Now, let's move on to the next value, x = -12:
Substituting x = -12 into the equation, we have:
-2(-12)^2 - 3(-12) + 2 = 0
Simplifying this, we get:
-2(144) + 36 + 2 = 0
-288 + 36 + 2 = 0
-252 + 2 = 0
-250 = 0
Since -250 does not equal 0, the equation is false for x = -12.
Finally, let's test the last value, x = 12:
Substituting x = 12 into the equation, we have:
-2(12)^2 - 3(12) + 2 = 0
Simplifying this, we get:
-2(144) - 36 + 2 = 0
-288 - 36 + 2 = 0
-324 + 2 = 0
-322 = 0
Since -322 does not equal 0, the equation is false for x = 12.
Based on our evaluations, none of the given values, -34, -12, and 12, are solutions to the quadratic equation −2x^2−3x+2=0. Therefore, none of these values are in the solution set. The answer provided in the question, "Only x=" is incomplete.
To determine whether a given value is a solution for the quadratic equation −2x^2−3x+2=0, we substitute the value into the equation and evaluate whether it makes the equation true.
Let's complete the table for the given values of x:
x | Substituted | Evaluate | True Statement?
___________________________________________________
−34 |-2(-34)^2−3(-34)+2=0 |False| No
−12 |-2(-12)^2−3(-12)+2=0 |False| No
12 |-2(12)^2−3(12)+2=0 |True | Yes
From the table, we can see that only x=12 is a solution to the quadratic equation.
To determine if the given values are solutions to the quadratic equation −2x^2−3x+2=0, we need to substitute them into the equation and evaluate them.
Using the given values:
For x = -34:
Substituting x = -34 into the equation, we get:
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2208
The result is not equal to 0, so x = -34 is not a solution.
For x = -12:
Substituting x = -12 into the equation, we get:
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250
The result is not equal to 0, so x = -12 is not a solution.
For x = 12:
Substituting x = 12 into the equation, we get:
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322
The result is not equal to 0, so x = 12 is not a solution.
Therefore, from the given values, only x = is in the solution set of the quadratic equation.