To determine the accuracy of the solutions provided by Jamal and George, we need to analyze their work and see if it aligns with the steps used to solve quadratic equations.
Analyzing Jamal's solution:
1. Jamal correctly sets the equation equal to 0 and writes it as x^2+4x−12=0.
2. Jamal factors the quadratic equation correctly as (x+6)(x−2)=0.
3. Jamal sets each factor equal to 0, x+6=0 and x−2=0.
4. Jamal solves each equation correctly, identifying x=-6 and x=2 as the solutions.
Analyzing George's solution:
1. George starts with the correct equation x^2+4x−5=7.
2. George also successfully factors the quadratic equation as (x+5)(x−1)=7.
3. George sets each factor equal to 0, x+5=0 and x−1=0.
4. However, George's error occurs in step 4 where he incorrectly states that x=-5 and x=1 are the solutions.
From our analysis, we can see that Jamal's solution is accurate because he correctly follows the steps to solve a quadratic equation. He factors the equation correctly, sets the factors equal to 0 properly, and solves the equations accurately to find the correct solutions.
George's solution, on the other hand, is inaccurate because he incorrectly identifies the solutions. He made an error in step 4 by incorrectly stating the values x=-5 and x=1 as the solutions, which is not accurate based on the given equation.
Therefore, we can conclude that Jamal's solution is accurate, while George's solution is inaccurate.
Jamal%0D%0AStep 1: Set equation =0%0D%0A=%0D%0A0%0D%0A .%09 x2+4x−12=0%0D%0A%0D%0A2%0D%0A+%0D%0A4%0D%0A%0D%0A−%0D%0A12%0D%0A=%0D%0A0%0D%0A %0D%0AStep 2: Write quadratic equation as the product of two factors.%09 (x+6)(x−2)=0%0D%0A(%0D%0A%0D%0A+%0D%0A6%0D%0A)%0D%0A(%0D%0A%0D%0A−%0D%0A2%0D%0A)%0D%0A=%0D%0A0%0D%0A %0D%0AStep 3: Set each factor equal to 0.%09 x+6=0%0D%0A%0D%0A+%0D%0A6%0D%0A=%0D%0A0%0D%0A and x−2=0%0D%0A%0D%0A−%0D%0A2%0D%0A=%0D%0A0%0D%0A %0D%0AStep 4: Solve each equation.%09 x=−6%0D%0A%0D%0A=%0D%0A−%0D%0A6%0D%0A and x=2%0D%0A%0D%0A=%0D%0A2%0D%0A George%0D%0AStep 1: Begin with the equation.%09 x2+4x−5=7%0D%0A%0D%0A2%0D%0A+%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A=%0D%0A7%0D%0A %0D%0AStep 2: Write quadratic equation as the product of two factors.%09 (x+5)(x−1)=7%0D%0A(%0D%0A%0D%0A+%0D%0A5%0D%0A)%0D%0A(%0D%0A%0D%0A−%0D%0A1%0D%0A)%0D%0A=%0D%0A7%0D%0A %0D%0AStep 3: Set each factor equal to 0.%09 x+5=0%0D%0A%0D%0A+%0D%0A5%0D%0A=%0D%0A0%0D%0A and x−1=0%0D%0A%0D%0A−%0D%0A1%0D%0A=%0D%0A0%0D%0A %0D%0AStep 4: Solve each equation.%09 x=−5%0D%0A%0D%0A=%0D%0A−%0D%0A5%0D%0A and x=1%0D%0A%0D%0A=%0D%0A1%0D%0A %0D%0AWhen trying to solve the quadratic equation x2+4x−5=7%0D%0A%0D%0A2%0D%0A+%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A=%0D%0A7%0D%0A , 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
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