Jamal

Question

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.

(2 points)

Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is very clear.

The answer is fully supported by details.

There may be a few errors in grammar, usage, or mechanics. Errors do not interfere with meaning.

1
The answer is somewhat clear.

Details are weak or not related.

There are some errors in grammar, usage, and mechanics. Errors interfere with meaning.

0 The question is not answered.
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say it all in word form even the numbers and signs

Answer 1

To determine which student provided the correct solution, we first need to analyze their work based on the equations presented.

Jamal started with the equation x squared plus four x minus twelve equals zero. He accurately rewrote this equation as the product of two factors, (x plus six)(x minus two) equals zero. By applying the Zero Product Property, he set each factor equal to zero. The solutions he found were x equals negative six and x equals two, which are correct for his equation.

On the other hand, George began with the equation x squared plus four x minus five equals seven. He appears to have incorrectly set up his equation as (x plus five)(x minus one) equals seven. Not only is this setup inaccurate because he failed to first rearrange the equation to set it equal to zero (the correct step would have been to move seven to the left side to obtain x squared plus four x minus twelve equals zero), but he also yielded incorrect factors for a different equation. Therefore, when George applied the Zero Product Property and solved for the factors, his solutions of x equals negative five and x equals one do not pertain to the original equation he was trying to solve.

In conclusion, Jamal's solution is accurate because he correctly factored his equation and applied the Zero Product Property to find the proper roots. In contrast, George's solution is inaccurate due to his initial error in setting up the quadratic equation, leading to incorrect factors and ultimately incorrect solutions.