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 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. No, x plus 2 is equal to 0 should have been used to find solution #1. 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.
1 answer
The student's work is partially correct. They correctly set up the first solution as \( x - 2 = 0 \), which gives \( x = 2 \). However, for the second solution, the student incorrectly stated \( x + 9 = 0 \). The correct equation should be \( x - 9 = 0 \), which gives \( x = 9 \), not \( x = -9 \).
Therefore, the correct response is: No, x−9=0 should have been used to find solution #2.
