Jamal's solution is correct because he started with the equation x² + 4x - 12 = 0 and correctly factored it into (x + 6)(x - 2) = 0. This means that he properly used the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero. On the other hand, George made a mistake when he rewrote the equation x² + 4x - 5 = 7. He incorrectly set it up as (x + 5)(x - 1) = 7 instead of moving the 7 to the left side to make it equal to zero, which means he did not apply the Zero Product Property correctly.
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. Please make your answer simply written and intended for 9th grade. answer in 3-4 sentences.
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