Question
1. Use the table to complete the statement.
x Substituted Evaluate True Statement?
−34
−
3
4
−12
−
1
2
12
1
2
(1 point)
For the quadratic equation −2x2−3x+2=0
−
2
2
−
3
+
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. Only x =
=
is in the solution set.
x Substituted Evaluate True Statement?
−34
−
3
4
−12
−
1
2
12
1
2
(1 point)
For the quadratic equation −2x2−3x+2=0
−
2
2
−
3
+
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. Only x =
=
is in the solution set.
Answers
GPT-4o mini
To determine which of the given values \( x = -34, -12, 12 \) is a solution to the quadratic equation \( -2x^2 - 3x + 2 = 0 \), we will substitute each value into the equation and evaluate it.
Let's evaluate each value step by step:
1. **For \( x = -34 \):**
\[
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2
\]
\[
= -2312 + 102 + 2
\]
\[
= -2312 + 104 = -2208 \quad (not \: = 0)
\]
2. **For \( x = -12 \):**
\[
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2
\]
\[
= -288 + 36 + 2
\]
\[
= -288 + 38 = -250 \quad (not \: = 0)
\]
3. **For \( x = 12 \):**
\[
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2
\]
\[
= -288 - 36 + 2
\]
\[
= -288 - 34 = -322 \quad (not \: = 0)
\]
Now that we have evaluated the function at all given values, we can conclude:
None of the substitutions yield 0, which means they are not solutions to the equation.
So the completed statement would be:
Only \( x = \text{none} \) is in the solution set.
Let's evaluate each value step by step:
1. **For \( x = -34 \):**
\[
-2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2
\]
\[
= -2312 + 102 + 2
\]
\[
= -2312 + 104 = -2208 \quad (not \: = 0)
\]
2. **For \( x = -12 \):**
\[
-2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2
\]
\[
= -288 + 36 + 2
\]
\[
= -288 + 38 = -250 \quad (not \: = 0)
\]
3. **For \( x = 12 \):**
\[
-2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2
\]
\[
= -288 - 36 + 2
\]
\[
= -288 - 34 = -322 \quad (not \: = 0)
\]
Now that we have evaluated the function at all given values, we can conclude:
None of the substitutions yield 0, which means they are not solutions to the equation.
So the completed statement would be:
Only \( x = \text{none} \) is in the solution set.