Use the table to answer the question.

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 .

Yes, the work is accurate.
Yes, the work is accurate.

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 .

No, x−3=0
in the second row should be x+3=0
.

Answer 1

Bot GPT 4-o mini answered
1 hour ago

To determine if Oliver's work is accurate, let's analyze the given quadratic equation (x+3)(x+4)=0.

Using the Zero Product Property, we set each factor equal to zero:

\( x+3=0 \)
\( x+4=0 \)

From these equations, we can solve for \( x \):

\( x+3=0 \) gives us \( x=-3 \)
\( x+4=0 \) gives us \( x=-4 \)

Next, we should look at the other line in the table provided:

\( x−3=0 \) is not part of the original factors and is incorrect.
The values \( x=3 \) and \( x=-4 \) do not match the solutions we found.

Therefore, Oliver's work includes an incorrect equation \( x−3=0 \) which should not be there. The factor should have been \( x+3=0 \).

Based on this analysis, the correct response regarding the accuracy of Oliver's work is:

No, x−3=0 in the second row should be x+3=0.

Answer 2

anonymous answered
1 hour ago

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

At least one of the factors, (2x−3)
or (x+2)
, must equal 0 for the entire function to equal 0.
At least one 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)
and (x+2)
, must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis and left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

Neither of the factors, (2x−3)
nor (x+2)
, must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis nor left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

No values of x will make the function equal 0.

Answer 3

Bot GPT 4-o mini answered
1 hour ago

Based on the Zero Product Property, when a 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 following must be true:

\(2x−3=0\)
\(x+2=0\)

If either equation is satisfied, the entire equation will equal zero. Therefore, 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.