Question

When trying to solve the quadratic equation x^2+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.

Answer 1

To evaluate Jamal and George's solutions for the quadratic equation
`\(x^2 + 4x - 5 = 7\)`, let's examine their work.

Jamal's Solution:

`\[ x^2 + 4x - 5 - 7 = 0 \]`

`\[ x^2 + 4x - 12 = 0 \]`

`\[ (x - 2)(x + 6) = 0 \]`

`\[ x = 2, -6 \]`

George's Solution:

`\[ x^2 + 4x - 5 - 7 = 0 \]`

`\[ x^2 + 4x - 12 = 0 \]`

`\[ (x - 3)(x + 4) = 0 \]`

`\[ x = 3, -4 \]`

The correct solutions are found by applying the Zero Product Property after step 2. Jamal's solution correctly factors the quadratic expression, resulting in the correct roots (x-values).

On the other hand, George's solution has an incorrect factorization, leading to inaccurate roots. Therefore, Jamal's solution is accurate, and George's solution is inaccurate due to an error in factorization.