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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Answer 1

To evaluate the accuracy of Jamal and George's solutions, we need to analyze their steps and adherence to the correct method for solving the quadratic equation.

Jamal begins with the equation \( x^2 + 4x - 12 = 0 \). He correctly factors it into \( (x + 6)(x - 2) = 0 \) and subsequently finds the solutions \( x = -6 \) and \( x = 2 \). This is a valid approach because after factoring the quadratic, each factor is set to zero using the Zero Product Property, leading to accurate solutions.

In contrast, George starts with the equation \( x^2 + 4x - 5 = 7 \) but makes an error right from the beginning by not isolating the variable correctly. The first step should be to rearrange the equation to standard form: \( x^2 + 4x - 5 - 7 = 0 \), simplifying to \( x^2 + 4x - 12 = 0 \). His incorrect factoring of \( (x + 5)(x - 1) = 7 \) does not correctly reflect the equation, and as a result, his solutions \( x = -5 \) and \( x = 1 \) are also incorrect.

In conclusion, Jamal's approach is accurate because he began with a properly formed quadratic equation and correctly applied the Zero Product Property to find the roots. On the other hand, George's solution is inaccurate due to an initial error in rearranging the equation, which led to the wrong factoring and ultimately false solutions.