Question

Use the tables to answer the question.

When trying to solve the quadratic equation x2+4x−5=7
, Jamal and George each provided their work in the tables.

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: Set equation = 0 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

Which student is incorrect? Explain how you know that his solution is inaccurate.

(2 points)

Answer 1

To determine which student is incorrect, we must carefully analyze each student's work to identify any errors in their calculations or factoring.

### Jamal's Work:
1. **Step 1**: Correctly set the equation to 0:
\[
x^2 + 4x - 5 - 7 = 0 \Longrightarrow x^2 + 4x - 12 = 0
\]
(This is correct).

2. **Step 2**: Factoring \(x^2 + 4x - 12 = 0\):
\[
(x + 6)(x - 2) = 0
\]
(This is also correct since \(6 \times (-2) = -12\) and \(6 + (-2) = 4\)).

3. **Step 3**: Setting each factor equal to 0:
\[
x + 6 = 0 \quad \text{and} \quad x - 2 = 0
\]

4. **Step 4**: Solving for \(x\):
\[
x = -6 \quad \text{and} \quad x = 2
\]

### George's Work:
1. **Step 1**: Did not correctly set the equation to 0:
\[
x^2 + 4x - 5 = 7 \Longrightarrow x^2 + 4x - 12 = 0
\]
- This step should match Jamal’s.

2. **Step 2**: Incorrectly factored the equation:
\[
(x + 5)(x - 1) = 7
\]
- This factored form is incorrect. The proper factors should result from the quadratic \(x^2 + 4x - 12\), which Jamal found correctly.

3. **Step 3**: Setting factors equal to 0 doesn’t apply since the factors are wrong.

4. **Step 4**: The solutions \(x = -5\) and \(x = 1\) derived from George’s incorrect factorization are also invalid.

### Conclusion:
**George is incorrect.** His initial factoring of the quadratic equation is flawed, as he did not provide the correct factors for \(x^2 + 4x - 12\). Instead of finding the accurate factors and roots, he has derived incorrect answers from incorrect premises. Therefore, the solutions he provided are not valid.