Kelly is correct and accurate because the linear factors result to zeros when substituted into the quadratic equation.
How to use zero product method in solving quadratic equation.
If one of the linear factors equals zero when substituted into the original quadratic equation, then the method is justified and the student is correct and accurate.
For Jill
x² + 2x - 15 = 9
Values of x are 3 and -5
Substitute
For x = -5
(-5)² + 2(-5) - 15 = 9
25 - 10 - 15 = 9
0 ≠ 9 (not true)
For x = 3
3² + 2(3) - 15 = 9
9 + 6 - 15 = 9
0 ≠ 9 (not true)
For Kelly
x² + 2x - 24 = 0
The values of x are -6 and 4
Substitute
For x = -6
(-6)² + 2(-6) - 24 = 0
36 -12 - 24 = 0
0 = 0(true)
For x = 4
4² + 2(4) - 24 = 0
16 + 8 - 24 = 0
0 = 0(correct)
Therefore, Kelly is correct and accurate because the linear factors result to zeros when substituted into the quadratic equation.