Anyone who is really passionate about maths?

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[quote="JDC6776"]

You should always write out your work.
Photocopy assignments before you turn them in, to make a study book for exams (you never know when you'll get it back).
Visualize the problems or relate them to a subject of interest if possible (it's easier with word problems cause you can just change the context)
Order of operations is the most critical thing to remember
Don't stress, frustration can block you mentally or withdraw you entirely
Sometimes you have to find your own way.


Aspies have no guarantee that their thinking is correct. Certainly no more guarantees than do NTs.

Aspies think -inside- a box quite often. It is just a different box from the NTs.

ruveyn

That will teach you to make absolute statements.

But then, where else but here will you get such a nice succinct rejoinder?



There are difficult questions within Mathematics that have no current answer and perhaps never will.

At Salome's LEVEL which is that of a novice, the questions that user may ask will be well within the capacities of the WP crowd to answer.

To help you lighten up I have included the following:

Way Cool!! !!

Ok so I got a bit sidetracked but been at it for a while now. There is a problem that I don't understand.
I typed it out in mathtype but it doesn't work to paste it here! It has exponents and such so I can't type it on here.
So frustrating, I need help with this!

Can you make a screenshot and post that?

I thought about it and wasn't too happy about putting it on my flickr. Now I'm thinking why not, it's not cheating or anything.

So the question on the top roughly translated is

Is the factorization below correct? If not, what is wrong?

[img][800:554]http://farm6.staticflickr.com/5328/9147325590_b8dd2d9d81_b.jpg[/img]


I follow the first three steps but then I'm completely lost. I would really appreciate it if someone could explain each step or give me a link to a video/page with similar problems.

It's past midnight where I am so I'll be going to bed now. I don't want anyone thinking I'm rude for not answering right away

i like math too,although i chose engineering for reason on getting a job.we actually do a lot of math there.But back to your question,the best way to get better at math you should exercise.Take the time you need exercising,and with the web you can find a lot of information,look khan academy or other math forums like wolfram.Look their advices and look their books.

looks correct to me but I defer to the experts on this site

Almost, you just have to multiply the final result by 2 (you divided everything by 2 at the very start, but forgot to account for it later). Unless of course f(x) is always equal to 0, in which case your answer would be right also.

Not quite.

Step 1 is correct. And so is the final solution. But do we really need to apply the quadratic formula and is it applied correctly?

Step 2 is correct if you think you can factor the equation
Can we?

We then need 2 numbers that when added up give -3 and when multiplied give -10
One of them needs to be a negative number.
What are the factors of 10?
1 2 5 10
Do any of these add up to - 3 if one of them is a negative number?
Yes
-5 and 2

Therefore we can factor this equation
(x-5)(x+2)


Instead, the solution choses to apply the quadratic formula in step 3. In that case, it's wrong to divide by 2 as is done in step 2. But if we don't divide by 2 and apply the quadratic formula, we get the same solution.

Does that make sense?

It would help to derive the famous quadratic formula.

We can assume without loss of generality that the equation is

x^2 +b*x + c = 0 (if x has a non zero co-efficient we can always divide through by that coefficient).

x^2 + b*x = -c

Now complete the square and get
x^2 + b*x + b^2/4 = -c + b^2/4 = (-4*c + b^2)/4

(x + b/2)^2 = (b^2 - 4*c)/4

take the square root of both sides:

(x + b/2) = +- sqrt(b^2 - 4*c)/2

move the b/2 to the other side

x = -b/2 +- sqrt(b^2 - 4*c)/2

and we are done

The factorization is incorrect, although it's only a small step away from being correct. What they end up with is 1/2 f(x) instead of f(x). Dividing by 2 as they did is perfectly legitimate, but if you do it you have to remember that you're solving for a different expression. Probably the best way to remember this is just to give a name to the new expression, say g(x). Then say that g(x) = 1/2 f(x), and when you're done solving for g(x), you're less likely to forget that g(x) isn't what you really want.

Going from step 3 to step 4 looks like it uses the quadratic formula and then performs some other operations at the same time for reasons that aren't clear to me. Maybe they think they're simplifying it, but it doesn't look simpler to me. Maybe they're using a slightly different format for the quadratic equation than I'm used to.

In any case, the quadratic formula could be used directly on f(x) if you have a version that has the variable a as well as b and c in it. A version like ruveyn's only has b and c in it, and just assumes that a = 1, but that works fine if you divide by a to get a new quadratic where a = 1 (and the new b and c are slightly different), which is exactly what the picture is doing.

You can always check whether a factorization is correct by just multiplying it out and seeing if you get back out what you originally put in.

Thank you for your answers everyone!
I still don't understand why it needs to be fractionated in the first place?
I'll read all of your comments again and see if I missed something.I'm not a natural at maths so I usually need to read the explanations a couple of times and then ponder them for a while. I'd say it's all greek to me but greek is actually easier for me to understand

Usually, you're more interested in calculating the zeros than in explicitly writing down the factorization. But the factorization is a very convenient way to notate the polynomial (that is, the function), so the zeros can be read out quickly.

Solving quadratic equations is something you need to do very often – in elementary physics, for example.

This video looks quite good (though I didn't watch it entirely):
http://www.mathhelp.com/lessons/secure/free_math_lesson-v2.php?id=2098&brand=ytfree&lp=ls

If you want to graph the function, you´ll need to calculate where (or if) the graph crosses the x-axis where y is 0 and therefore f(x) = 0. You can only find out mathematically by factoring the equation.
Once you´ve done that, the rest is easy by writing the equation
(x-5)(x+2)=0

Because it is a multiplication, you can set both terms to zero seperately:

x-5=0
x+2=0

Now you can easily solve for f(x) = 0