To determine the accuracy of each student's solution, we can check if their final solutions satisfy the original equation.
For Jamal's solution:
The equation is x^2 + 4x - 12 = 0, and he factored it as (x + 6)(x - 2) = 0.
Setting each factor equal to 0, he obtained x + 6 = 0 and x - 2 = 0.
Solving each equation, he found x = -6 and x = 2.
To check his solution, we substitute these values back into the original equation:
For x = -6: (-6)^2 + 4(-6) - 12 = 0, which is true.
For x = 2: (2)^2 + 4(2) - 12 = 0, which is also true.
Since both values satisfy the original equation, we can conclude that Jamal's solution is accurate.
For George's solution:
The equation is x^2 + 4x - 5 = 7, and he factored it as (x + 5)(x - 1) = 7.
Setting each factor equal to 0, he obtained x + 5 = 0 and x - 1 = 0.
Solving each equation, he found x = -5 and x = 1.
To check his solution, we substitute these values back into the original equation:
For x = -5: (-5)^2 + 4(-5) - 5 = 10 - 20 - 5 = -15, which is not equal to 7.
For x = 1: (1)^2 + 4(1) - 5 = 1 + 4 - 5 = 0, which is not equal to 7.
Since both values do not satisfy the original equation, we can conclude that 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.
2 answers
where did george first go wrong in his steps
1 answer