Question
Solution Sets of Quadratic Equations Quick Check
3 of 53 of 5 Items
Question
Ariel is trying to determine if x=−3 is a solution to the quadratic equation −3x2−9x=0. Which explanation demonstrates the correct reasoning?(1 point)
Responses
Yes, x=−3 is a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 0=0 TrueYes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 0 equals 0 True
No, x=−3 is not a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 54≠0 FalseNo, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 does not equal 0 False
Yes, x=−3 is a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 54=0 TrueYes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 equals 0 True
No, x=−3 is not a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 −54≠0 FalseNo, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 negative 54 does not equal 0 False
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3 of 53 of 5 Items
Question
Ariel is trying to determine if x=−3 is a solution to the quadratic equation −3x2−9x=0. Which explanation demonstrates the correct reasoning?(1 point)
Responses
Yes, x=−3 is a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 0=0 TrueYes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 0 equals 0 True
No, x=−3 is not a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 54≠0 FalseNo, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 does not equal 0 False
Yes, x=−3 is a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 54=0 TrueYes, x equals negative 3 is a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 54 equals 0 True
No, x=−3 is not a solution because substituting it back into the equation results in the following:
x Substituted Evaluate True Statement?
−3 −3(−3)2−9(−3)=0 −54≠0 FalseNo, x equals negative 3 is not a solution because substituting it back into the equation results in the following: x Substituted Evaluate True Statement? negative 3 negative 3 left parenthesis negative 3 right parenthesis squared minus 9 left parenthesis negative 3 right parenthesis equals 0 negative 54 does not equal 0 False
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine whether \( x = -3 \) is a solution to the quadratic equation \( -3x^2 - 9x = 0 \), we can substitute \( x = -3 \) into the equation and evaluate.
Starting with the equation:
\[
-3x^2 - 9x = 0
\]
Substituting \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Calculating:
1. Compute \( (-3)^2 = 9 \).
2. Substitute this value into the equation:
\[
-3(9) - 9(-3) = 0
\]
3. Simplify:
\[
-27 + 27 = 0
\]
This simplifies to:
\[
0 = 0
\]
Since both sides of the equation are equal, \( x = -3 \) is indeed a solution.
The correct response is:
**Yes, x = -3 is a solution because substituting it back into the equation results in the following:**
\[
-3(-3)^2 - 9(-3) = 0 \Rightarrow 0 = 0 \text{ (True)}
\]
Starting with the equation:
\[
-3x^2 - 9x = 0
\]
Substituting \( x = -3 \):
\[
-3(-3)^2 - 9(-3) = 0
\]
Calculating:
1. Compute \( (-3)^2 = 9 \).
2. Substitute this value into the equation:
\[
-3(9) - 9(-3) = 0
\]
3. Simplify:
\[
-27 + 27 = 0
\]
This simplifies to:
\[
0 = 0
\]
Since both sides of the equation are equal, \( x = -3 \) is indeed a solution.
The correct response is:
**Yes, x = -3 is a solution because substituting it back into the equation results in the following:**
\[
-3(-3)^2 - 9(-3) = 0 \Rightarrow 0 = 0 \text{ (True)}
\]
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