To verify the accuracy of the solutions, we can substitute the values of x obtained by each student back into the original equation and check if both sides of the equation are equal.
For Jamal's solution, x = -6 and x = 2.
Substituting x = -6 into the equation x² + 4x -12 = 0:
(-6)² + 4(-6) -12 = 36 -24 - 12 = 0
Since the left-hand side is equal to zero, Jamal's solution is accurate for the given equation.
Substituting x = 2 into the equation x² + 4x -12 = 0:
(2)² + 4(2) - 12 = 4 + 8 - 12 = 0
Again, the left-hand side is equal to zero, confirming that Jamal's solution is accurate for the given equation.
For George's solution, x = -5 and x = 1.
Substituting x = -5 into the equation x² + 4x -5 = 7:
(-5)² + 4(-5) -5 = 25 -20 - 5 = 0
The left-hand side is equal to zero, indicating that George's solution is accurate for the given equation.
Substituting x = 1 into the equation x² + 4x -5 = 7:
(1)² + 4(1) - 5 = 1 + 4 - 5 = 0
Once again, the left-hand side is equal to zero, confirming that George's solution is accurate for the given equation.
From the above analysis, it is clear that both solutions provided by Jamal and George are accurate for their respective equations.
Use the tables to answer the question.
Jamal
Step 1: Set equation = 0.
x? + 4х - 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.
x? + 4x - 5 = 7
Step 2: Write quadratic equation as the product of two factors.
（2+5） （2=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 x? + 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.
1 answer