Use the tables to answer the question. 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: 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.

Answer 1

From the given information, we know that Jamal and George both used the Zero Product Property to solve their respective quadratic equations in step 3. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

For Jamal's solution, the quadratic equation x^2 + 4x - 12 = 0 was factored into (x + 6)(x - 2) = 0. Setting each factor equal to zero gives x + 6 = 0 and x - 2 = 0. Solving these equations gives x = -6 and x = 2. To check if Jamal's solution is accurate, we can substitute these values back into the original equation x^2 + 4x - 12 = 0 and see if the equation holds true. If the equation holds true for both values, then Jamal's solution is accurate.

For George's solution, the quadratic equation x^2 + 4x - 5 = 7 was factored into (x + 5)(x - 1) = 7. Setting each factor equal to zero gives x + 5 = 0 and x - 1 = 0. Solving these equations gives x = -5 and x = 1. However, George made a mistake by adding 7 to both sides of the equation instead of subtracting it. To check if George's solution is accurate, we can substitute his values back into the original equation. If the equation does not hold true for both values, then George's solution is inaccurate.

Therefore, we can conclude that Jamal's solution is accurate, as it satisfies the original equation, while George's solution is inaccurate, as it does not satisfy the original equation.