Question
Use the table to answer the question.
(x+3)(x+4)=0
x−3=0 x+4=0
x=3 x=−4 While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4) equals 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?(1 point)
Responses
No, x+4=0 in the second row should be x−4=0.
No, x plus 4 equals 0 in the second row should be x minus 4 equals 0 .
No, he should have a third column where he should set x=0.
No, he should have a third column where he should set x equals 0 .
Yes, the work is accurate.
Yes, the work is accurate.
No, x−3=0 in the second row should be x+3=0.
(x+3)(x+4)=0
x−3=0 x+4=0
x=3 x=−4 While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4) equals 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?(1 point)
Responses
No, x+4=0 in the second row should be x−4=0.
No, x plus 4 equals 0 in the second row should be x minus 4 equals 0 .
No, he should have a third column where he should set x=0.
No, he should have a third column where he should set x equals 0 .
Yes, the work is accurate.
Yes, the work is accurate.
No, x−3=0 in the second row should be x+3=0.
Answers
Answer
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0 ?(1 point)
Responses
No values of x will make the function equal 0.
No values of x will make the function equal 0.
Neither of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.
Both factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.
At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Responses
No values of x will make the function equal 0.
No values of x will make the function equal 0.
Neither of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.
Both factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.
At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.
Answered by
GPT-4o mini
To evaluate whether Oliver's work is accurate, we need to apply the Zero Product Property correctly to the equation \((x + 3)(x + 4) = 0\).
1. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be equal to zero.
2. Therefore, we set each factor equal to zero:
- \(x + 3 = 0\)
- \(x + 4 = 0\)
3. Solving these equations gives:
- From \(x + 3 = 0\), we find \(x = -3\).
- From \(x + 4 = 0\), we find \(x = -4\).
Now let's examine Oliver's work according to the provided options:
- The second row mistakenly includes \(x - 4 = 0\), which is incorrect because it should be \(x + 4 = 0\).
- Thus, the conclusion that \(x = -4\) also has an error in its presentation in the table.
Therefore, based on the mistakes identified, the correct answer to whether Oliver's work is accurate is:
**No, x+4=0 in the second row should be x−4=0.**
1. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be equal to zero.
2. Therefore, we set each factor equal to zero:
- \(x + 3 = 0\)
- \(x + 4 = 0\)
3. Solving these equations gives:
- From \(x + 3 = 0\), we find \(x = -3\).
- From \(x + 4 = 0\), we find \(x = -4\).
Now let's examine Oliver's work according to the provided options:
- The second row mistakenly includes \(x - 4 = 0\), which is incorrect because it should be \(x + 4 = 0\).
- Thus, the conclusion that \(x = -4\) also has an error in its presentation in the table.
Therefore, based on the mistakes identified, the correct answer to whether Oliver's work is accurate is:
**No, x+4=0 in the second row should be x−4=0.**
Answered by
GPT-4o mini
According to the Zero Product Property, if the product of two factors equals zero, at least one of the factors must be zero.
For the quadratic equation \((2x - 3)(x + 2) = 0\), this means that:
- **At least one of the factors, \(2x - 3\) or \(x + 2\), must equal 0 for the entire function to equal 0.**
We can find the values of \(x\) that make the expression equal to zero by setting each factor equal to zero:
1. From \(2x - 3 = 0\), we solve for \(x\):
- \(2x = 3\)
- \(x = \frac{3}{2}\)
2. From \(x + 2 = 0\), we solve for \(x\):
- \(x = -2\)
Both factors lead to valid solutions, confirming that at least one of the factors must equal zero for the product to be zero.
Thus, the correct statement is:
**At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.**
For the quadratic equation \((2x - 3)(x + 2) = 0\), this means that:
- **At least one of the factors, \(2x - 3\) or \(x + 2\), must equal 0 for the entire function to equal 0.**
We can find the values of \(x\) that make the expression equal to zero by setting each factor equal to zero:
1. From \(2x - 3 = 0\), we solve for \(x\):
- \(2x = 3\)
- \(x = \frac{3}{2}\)
2. From \(x + 2 = 0\), we solve for \(x\):
- \(x = -2\)
Both factors lead to valid solutions, confirming that at least one of the factors must equal zero for the product to be zero.
Thus, the correct statement is:
**At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.**
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