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 students work correct?

Question

ORGINAL equation: (x-2)(x-9)=0
Solution #1: x-2 = 0
X = 2
Solution #2: x+9 = 0
X= -9
A. Yes the student answered the problem correctly
B. No there should be #3
C. No, x + 2 = 0 should have been used to find solution #1
D. No, x - 9 = 0 should have been used to find solution #2

Answer 1

The student's work is not correct. The correct analysis using the zero product property includes the following steps:

1. Set each factor equal to zero.
   • From \( (x-2) = 0 \) → \( x = 2 \)
   • From \( (x-9) = 0 \) → \( x = 9 \)

However, the student made a mistake in identifying the second solution. The correct equation should be \( x - 9 = 0 \), which gives \( x = 9 \), not \( x + 9 = 0 \).

Therefore, the correct answer is:

D. No, x - 9 = 0 should have been used to find solution #2.