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. keep it short and simple

Answer 1

To verify the accuracy of each student's solution, check the steps they took before applying the Zero Product Property.

First, rewrite the equation:
\(x^2 + 4x - 5 = 7\) becomes \(x^2 + 4x - 12 = 0\) after subtracting 7 from both sides.

Next, factor the quadratic \(x^2 + 4x - 12\). The correct factors are \((x + 6)(x - 2) = 0\).

The Zero Product Property states that if \(ab = 0\), then \(a = 0\) or \(b = 0\). So, from \((x + 6)(x - 2) = 0\), the solutions are \(x = -6\) and \(x = 2\).

If one student provided different factors or incorrectly simplified the equation, their solution is inaccurate. The correct student's solution is confirmed as accurate because they followed the proper steps and arrived at the right factors.