Question
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (5x+1)(x−8)=0
?(1 point)
Responses
At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
No values of x will make the left side of the equation equal 0.
?(1 point)
Responses
At least one of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
At least one of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, (5x+1)
or (x−8)
, must equal 0 for the left side of the equation to equal 0.
Neither of the factors, open paren 5 x plus 1 close paren or open paren x minus 8 close paren, must equal 0 for the left side of the equation to equal 0.
No values of x will make the left side of the equation equal 0.
Answers
GPT-4o mini
Based on the Zero Product Property, the correct statement regarding the quadratic equation \((5x+1)(x−8)=0\) is:
**At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.**
This is true because the Zero Product Property states that if the product of two factors equals zero, then at least one of the factors must be equal to zero.
**At least one of the factors, (5x+1) or (x−8), must equal 0 for the left side of the equation to equal 0.**
This is true because the Zero Product Property states that if the product of two factors equals zero, then at least one of the factors must be equal to zero.
While using the Zero Product Property to find the solutions for the quadratic equation (x−2)(x−9)=0
, a student completed the work below. Is the student's work correct?
(x−2)(x−9)=0
original equation
Solution #1:
x−2=0
x=2
Solution #2:
x+9=0
x=−9
(1 point)
Responses
No, x−9=0
should have been used to find solution #2.
No, x minus 9 is equal to 0 should have been used to find solution #2.
No, there should be a solution #3.
No, there should be a solution #3.
Yes, the student answered the problem correctly.
Yes, the student answered the problem correctly.
No, x+2=0
should have been used to find solution #1.
, a student completed the work below. Is the student's work correct?
(x−2)(x−9)=0
original equation
Solution #1:
x−2=0
x=2
Solution #2:
x+9=0
x=−9
(1 point)
Responses
No, x−9=0
should have been used to find solution #2.
No, x minus 9 is equal to 0 should have been used to find solution #2.
No, there should be a solution #3.
No, there should be a solution #3.
Yes, the student answered the problem correctly.
Yes, the student answered the problem correctly.
No, x+2=0
should have been used to find solution #1.
GPT-4o mini
The student's work contains an error. The correct application of the Zero Product Property requires solving each factor separately. The first factor is correctly solved:
1. **Solution #1:**
\[
x - 2 = 0 \implies x = 2
\]
However, in the second solution the student incorrectly stated:
2. **Solution #2:**
(Incorrectly stating \(x + 9 = 0\))
The correct equation should be:
\[
x - 9 = 0 \implies x = 9
\]
Thus, the correct answer is:
**No, x−9=0 should have been used to find solution #2.**
1. **Solution #1:**
\[
x - 2 = 0 \implies x = 2
\]
However, in the second solution the student incorrectly stated:
2. **Solution #2:**
(Incorrectly stating \(x + 9 = 0\))
The correct equation should be:
\[
x - 9 = 0 \implies x = 9
\]
Thus, the correct answer is:
**No, x−9=0 should have been used to find solution #2.**
Solve the quadratic equation (x+6)(x−4)=0
using the Zero Product Property.(1 point)
Responses
The solution set is {−4, 6}
.
The solution set is {−4, 6}
.
The solution set is {0, 2}
.
The solution set is {0, 2}
.
The solution set is {−6, 4}
.
The solution set is {−6, 4}
.
There are no solutions to this equation.
There are no solutions to this equation.
using the Zero Product Property.(1 point)
Responses
The solution set is {−4, 6}
.
The solution set is {−4, 6}
.
The solution set is {0, 2}
.
The solution set is {0, 2}
.
The solution set is {−6, 4}
.
The solution set is {−6, 4}
.
There are no solutions to this equation.
There are no solutions to this equation.
GPT-4o mini
To solve the quadratic equation \((x+6)(x−4)=0\) using the Zero Product Property, we set each factor equal to zero:
1. Set \(x + 6 = 0\):
\[
x = -6
\]
2. Set \(x - 4 = 0\):
\[
x = 4
\]
Therefore, the solutions are \(x = -6\) and \(x = 4\).
The solution set is \(\{-6, 4\}\).
So, the correct response is:
**The solution set is {−6, 4}.**
1. Set \(x + 6 = 0\):
\[
x = -6
\]
2. Set \(x - 4 = 0\):
\[
x = 4
\]
Therefore, the solutions are \(x = -6\) and \(x = 4\).
The solution set is \(\{-6, 4\}\).
So, the correct response is:
**The solution set is {−6, 4}.**
Solve the quadratic equation 5x(x+12)=0
using the Zero Product Property.(1 point)
Responses
The solution set is x={−12, 0}
.
The solution set is x={−12, 0}
.
The solution set is x={0, 12}
.
The solution set is x={0, 12}
.
The solution set is x={5, 12}
.
The solution set is x={5, 12}
.
The solution set is x={1/12, 1/5}
.
The solution set is x={1/12, 1/5}
.
using the Zero Product Property.(1 point)
Responses
The solution set is x={−12, 0}
.
The solution set is x={−12, 0}
.
The solution set is x={0, 12}
.
The solution set is x={0, 12}
.
The solution set is x={5, 12}
.
The solution set is x={5, 12}
.
The solution set is x={1/12, 1/5}
.
The solution set is x={1/12, 1/5}
.
GPT-4o mini
To solve the quadratic equation \(5x(x + 12) = 0\) using the Zero Product Property, we set each factor equal to zero:
1. Set \(5x = 0\):
\[
x = 0
\]
2. Set \(x + 12 = 0\):
\[
x = -12
\]
Thus, the solutions are \(x = 0\) and \(x = -12\).
The solution set is \(\{-12, 0\}\).
So, the correct response is:
**The solution set is x={−12, 0}.**
1. Set \(5x = 0\):
\[
x = 0
\]
2. Set \(x + 12 = 0\):
\[
x = -12
\]
Thus, the solutions are \(x = 0\) and \(x = -12\).
The solution set is \(\{-12, 0\}\).
So, the correct response is:
**The solution set is x={−12, 0}.**