- #1
Imparcticle
- 573
- 4
We were recently reviewing quadratic equations in my algebra 1 class. As my teacher simplified equation after equation on the board, I began to get this nagging feeling there was something incorrect.
I have pin pointed where I believe an error was made.
At this point in solving a quadratic equation, (6 +/- 2 root24)/2, my teacher simply cancels out the 6 and the 2 at once. I disagree here. It is a rule that you cannot cancel each component of an equation where a term is separated by a + or - sign (of course, one can cancel the two since it is being multiplied with the "root24"). Instead, it I believe one must factor out a 2 from the numerator, then cancel out the 2 in the denominator.
my way:
1.)
6 +/- 2 root24 2(3 +/- root24)
-------------- = ---------------- = 3 +/- root24
2 2
2.)
The way my teacher does it:
6 +/- 2 root24 6/2 +/- 2/2 root24 = 3 +/- root24
--------------=
2
I realize that essentially, when you factor (as I did) , you are dividing each term, seperately by 2. However on the second example, one is dividing each term by the exact same integer.
is my analysis correct or incorrect?
I have pin pointed where I believe an error was made.
At this point in solving a quadratic equation, (6 +/- 2 root24)/2, my teacher simply cancels out the 6 and the 2 at once. I disagree here. It is a rule that you cannot cancel each component of an equation where a term is separated by a + or - sign (of course, one can cancel the two since it is being multiplied with the "root24"). Instead, it I believe one must factor out a 2 from the numerator, then cancel out the 2 in the denominator.
my way:
1.)
6 +/- 2 root24 2(3 +/- root24)
-------------- = ---------------- = 3 +/- root24
2 2
2.)
The way my teacher does it:
6 +/- 2 root24 6/2 +/- 2/2 root24 = 3 +/- root24
--------------=
2
I realize that essentially, when you factor (as I did) , you are dividing each term, seperately by 2. However on the second example, one is dividing each term by the exact same integer.
is my analysis correct or incorrect?