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. make it as short as possible
The correct student's solution is accurate because they correctly applied the Zero Product Property in step 3 which states that if a product of factors equals zero, then at least one of the factors must be zero. They then solved the resulting equations correctly in step 4.
The incorrect student's solution is inaccurate because they did not apply the Zero Product Property correctly in step 3. They incorrectly set the factors equal to 7 instead of 0. This resulted in incorrect solutions in step 4.
The correct student's solution is accurate because they correctly applied the Zero Product Property in step 3 of the process and obtained the correct solutions for x. Additionally, their equation factors and matches the original equation.
The incorrect student's solution is inaccurate because they did not correctly apply the Zero Product Property in step 3. They set each factor equal to 7 instead of 0, resulting in incorrect solutions for x.
To determine the accuracy of the solutions, you can analyze step 3 of the process. The correct student, Jamal, correctly sets each factor of the quadratic equation (x+6)(x-2)=0 equal to zero (x+6=0 and x-2=0). This is a crucial step in applying the Zero Product Property. If either factor is not set equal to zero, the solution would not be accurate.
On the other hand, the incorrect student, George, mistakenly sets the factors (x+5) and (x-1) equal to the constant term 7 instead of zero. This error invalidates his solution because the Zero Product Property requires the equation to be set equal to zero before solving.
Therefore, based on the correct implementation of step 3, we can conclude that Jamal's solution is accurate, while George's solution is inaccurate.
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.
Who is correct and who is incorrect