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, 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−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, x+2=0
should have been used to find solution #1.

Answer 1

The student's work is not entirely correct.

The correct application of the Zero Product Property involves setting each factor equal to zero. The steps should be as follows:

1. From the equation \((x - 2)(x - 9) = 0\), the student correctly identified the first solution:

   • \(x - 2 = 0\) leads to \(x = 2\).

2. However, for the second factor, the student incorrectly wrote \(x + 9 = 0\). The correct factor should be \(x - 9 = 0\):

   • Setting \(x - 9 = 0\) gives \(x = 9\).

Thus, the solutions to the equation \((x - 2)(x - 9) = 0\) are \(x = 2\) and \(x = 9\).

Based on this, the most accurate response would be: No, x−9=0 should have been used to find solution #2.