Jamal
Step 1: Set equation =0 . x2+4x−12=0
Step 2: Write quadratic equation as the product of two factors. (x+6)(x−2)=0
Step 3: Set each factor equal to 0. x+6=0 and x−2=0
Step 4: Solve each equation. x=−6 and x=2
George
Step 1: Begin with the equation. x2+4x−5=7
Step 2: Write quadratic equation as the product of two factors. (x+5)(x−1)=7
Step 3: Set each factor equal to 0. x+5=0 and x−1=0
Step 4: Solve each equation. x=−5 and x=1
When trying to solve the quadratic equation x2+4x−5=7 , Jamal and George each provided their work in the tables. Each said they used the Zero Product Property to solve the equation after step 2. Explain how you know the correct student’s solution is accurate and how you know the incorrect student’s solution is inaccurate.
Who is correct and who is incorrect
In this case, Jamal is correct and George is incorrect.
Jamal correctly identified the two factors of the quadratic equation as (x+6) and (x-2), and correctly set each factor equal to zero. He then correctly solved for x and found that x can be either -6 or 2.
On the other hand, George made an error in step 2. He incorrectly wrote the quadratic equation as (x+5)(x-1)=7, instead of (x+5)(x-1)=0. By setting each factor equal to zero, he found that x can be either -5 or 1. However, this does not solve the original equation x^2+4x-5=7. Therefore, George's solution is inaccurate.