While using the Zero Product Property to find the solutions for the quadratic equation (x−2)(x−9)=0

Question

, 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+2=0
should have been used to find solution #1.
No, x plus 2 is equal to 0 should have been used to find solution #1.

No, there should be a solution #3.
No, there should be a solution #3.

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.

Yes, the student answered the problem correctly.

Answer 1

The student's work is not correct.

Here is the breakdown:

The original equation is \((x−2)(x−9)=0\).

According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. This means you set each factor equal to zero:

1. For the first factor: \[ x-2=0 \implies x=2 \]

2. For the second factor: \[ x-9=0 \implies x=9 \]

However, the student mistakenly wrote the second equation as \(x + 9 = 0\), which is incorrect. The correct equation should be \(x-9=0\).

Thus, the correct conclusion is: No, x−9=0 should have been used to find solution #2.