This is little different from many other types of problematic posts. The mods frequently have to make decisions on whether a post is hate speech, “being a jerk”, violative of US law, an unnecessary game thread, excessively argumentative, threatening, trolling and so on. One more thing isn’t going to kill them, especially something they’be been dealing with all along. Merely codifying a Board policy on this matter is not going to make any additional work for them.
Your denominator should be 2A, not 2AC. Otherwise, as far as I know, yes with the following caveat:
If your discriminant (that’s the part that goes b^2, or b[sup]2[/sup], minus 4AC, or simply the part under the sqrt sign) is negative, your results are not going to be real numbers. Real here is, from what I know, not exactly the same as the common meaning given to real. A real number is defined here. If your discriminant is not real, it will be imaginary (and thus in the form of a+bi, where a is a real number, b is the coefficient of i and i is the square root of -1), which is also defined (and linked) on that same page. ultrafilter might know of a more succinct definition, but for our purposes I think that one works well enough.
But regardless, what does this mean? It basically means that if you’re using a thinking machine (calc, computer, whatever) to figure the roots of a problem, it’s going to give you an error if you solutions to a quadratic equation are imaginary and it’s operating in real number mode. If you (can) change it to imaginary number mode (a+bi on a TI-X programmable calculator, where X could be several different numbers from I think the 80s up), you’ll get values such as this, for example:
4+5i
4-5i
That’s the display you’ll get, at least, from the quadratic programs I’ve written. It’s the simplest way I know to display such a beast.
-b± sqrt(b2 - 4ac)
x = ------------------
2ac
Yes, the c was a typo.
That’s a very useful formula! I wish I had known it when I was in school. It would have made things much easier. I wonder why we were never taught it?
Incidentally, I posted earlier that 4x[sup]2[/sup] - 15 + 9 didn’t look right. This is because I wasn’t looking hard enough. I figured out that it factors to (4x-3)(x-3), but dividing by (x-3) gave me .75 when I knew the “answer” was 3.
Yes, it’s a standard formula.
Yes, it is always true. (And your teachers absolutely should have shown it to you…several times. Many things in pre-calc are not going to make sense at all, if you don’t have that.)
Just to show work, if you have an equation:
ax[sup]2[/sup]+bx+c=0
you use the “completing the squares” rules on it -
so multiply by 4a to get
4a[sup]2[/sup]x[sup]2[/sup]+4abx+4ac=0
subtract 4ac from each side, and add b[sup]2[/sup] for:
4a[sup]2[/sup]x[sup]2[/sup]+4abx+ b[sup]2[/sup]= b[sup]2[/sup]-4ac
factor the left half
(2ax+b)[sup]2[/sup]=b[sup]2[/sup]-4ac
take the square roots -
2ax+b=sqrt(b[sup]2[/sup]-4ac)
and finish it to
-b± sqrt(b[sup]2[/sup] - 4ac)
x = ------------------
2a
Now I feel cheated. 
Question about “completing the squares”: Do you always multiply by 4a and add b[sup]2[/sup]? I mean, is that “part of the rule”?
Trig and pre-calc were the same class, so they were probably abbreviated.
I’d like to thank everyone for the assistance.
Uh… I do not know what he was talking about, myself.
Completing the square
ax^2 + bx = 0
Take b and divide by two, then square it:
(b/2)^2
Add to both sides:
x^2 + bx + (b/2)^2 = (b/2)^2
Which will equal:
(x+(b/2)^2)^2 = (b/2)^2
Hopefully this helps!
Thinking about it, I should just derive the quadratic formula.
ax^2 + bx + c = 0
Dividing by a:
x^2 + (b/a)x + (c/a) = 0
Subtracting (c/a):
x^2 + (b/a)x = -(c/a)
Completing the squares:
x^2 + (b/a)x + (b/2a)^2 = -(c/a) + (b/2a)^2
Which goes to:
(x + (b/2a))^2 = -(c/a) + (b^2/4a)
(x + (b/2a))^2 = (b^2 - 4ac)/(4a^2)
Take the sqrt:
x + (b/2a) = +/- sqrt(b^2-4ac)/(2a)
Subtracting, we get:
x = (-b/2a) + +/- sqrt(b^2-4ac)/(2a)
Or:
x = (-b +/- sqrt(b^2-4ac)) / 2a
This was fun, I am with the OP. (sorry for the hijak, though)
I’m guessing that part of the reason for the “homework rule” is to keep people from asking questions that absolutely no one cares about. If you don’t care about it except insofar as it allows you to complete an assignment, and you don’t think anyone else would find it even remotely interesting, don’t clutter up the message board with it.
I think math question are great. As long as they’re not just, “Here, solve these ten equations and don’t bother me with how you did it,” of course.
Yeah, there’s not much need to go into the specifics of what a real number is. That’s good enough.
No, I knew where I was going, so I multiplied to make the derivation easier.
As far as completing squares, sometimes factoring is harder to see.
But, every quadratic equation is equal to some linear equation squared plus a constant. So, instead solving for the quadratic, you figure out what the linear equation is, what the constant is, and then set the linear = to the positive and negative square roots of the constant…
so in the homework example …
original equation:
4x[sup]2[/sup]-15x+9=0
(4x[sup]2[/sup]-15x+225/16)-81/16=0
linear equation^2+constant:
(2x-15/4)[sup]2[/sup]-81/16=0
(2x-15/4)[sup]2[/sup]=81/16
2x-15/4=±9/4 or x=3/4, x=3
As a high school math teacher, I simply MUST butt in here.
The proofs for the formula:
x= (-b±sqrt(b^2-4ac))/2a
That amarinth and ZebraShaSha present are both correct - which proof you find easiest is entirely up to you.
And you ask if the multiplying by 4a and so firth is standard - the answer is yes. “a” denotes any given value in the ax^2+bx+c=0 equation. a could be 1 or 4, doesn’t matter which, the proof applies in all cases (which is why it’s more convenient to use the a, b and c in the first place).
I hope this made sense, if not, can I use the excuse that I’m not used to explaining this in english?
Tikster
If you read something like this, and feel compelled to point out that, no, if doesn’t apply in quite all cases (a can’t be 0)— you just might be a math geek!
(Of course, if a=0, it’s not really a quadratic equation, just a linear one, and you don’t need any fancy-schmancy quadratic formula to solve it.)
You are correct of course 
Good thing you’re not my pupil or I’d owe you cake!
Tikster
My Brain Hurts!
::Smashing bricks against sides of head::
My thinking is close to astro’s on this topic. I’d also like to add that no hijack is more painful than a math hijack. Kee-rist.
I love seeing math problems on the board here; it helps me remember what I’ve lost over the years. I think that the members here are not just “homework copiers”, but smart folks who just need a little bump here and there to solve something that’s stumped them for an inordinate amount of time. Also, I think there a quite a few people here who love to help those in need. Kinda builds up the health of the board when there is this type of exchange going on. I can see helping any of the charter members, but it can also attract new members when they see this type of exchange. Just so it doesn’t become a “finish my homework” session, I think the OP should always state what they have done so far with the problem as well as the problem itself.
Johnny LA’s problem can be solved so many ways, and I think the beauty here is that there were other posters who told how to do it those different ways. Johnny could pick the most comfortable way to approach the problem, or he could also study the other methods presented to increase his proficiency in dealing with future math problems that will inevitably come his way. That is what makes this board soooooo kewl.
Really? I’d think with some of the quick-draw artists we have that would be the express train to Closedthreadville, with a threat of banning if you try it again.
I was the guy who opened the homework thread that was closed. I asked for help in understanding how to answer the question, not simply for the answer!
So if you like math questions…and the kind people who replied to my thread did…then how are homework questions “questions that absoultely no one cares about”?
Sorry to clutter up your message board. I’ll clear threads and posts with you next time!
Make that maths questions…sloppy typing!
I never said they were, necessarily! I said they could be, and if they were, that was a reason not to post them. And I certainly didn’t mean to imply that your question fell into that category.