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

Answer 1

To determine which student's solution is accurate and which is inaccurate, we need to compare their solutions and reasoning.

Let's first look at Jamal's solution:

Step 1: x^2 + 4x − 5 = 7
Step 2: x^2 + 4x − 5 − 7 = 7 − 7 (subtract 7 from both sides)
Step 2 (simplified): x^2 + 4x − 12 = 0

Now, let's check George's solution:

Step 1: x^2 + 4x − 5 = 7
Step 2: x^2 + 4x = 7 + 5 (add 5 to both sides)
Step 2 (simplified): x^2 + 4x = 12

Comparing the two solutions, we can see that George made a mistake in his step 2. He incorrectly added 5 to both sides of the equation, resulting in the incorrect equation x^2 + 4x = 12. This mistake could lead to incorrect roots or solutions for the quadratic equation.

On the other hand, Jamal's solution is accurate. He correctly subtracted 7 from both sides of the equation, resulting in the equivalent equation x^2 + 4x − 12 = 0. This equation is in the correct form for solving a quadratic equation using the Zero Product Property.

Therefore, we can conclude that Jamal's solution is accurate, and George's solution is inaccurate.