Math Help Forum

Discuss anything not related to Armadillo Run here.

Moderator: Moderators

Postby Ikerous » Tue Nov 06, 2007 2:51 am

JustcallmeDrago wrote:x^2 + 4ax + 4a^2 - b^2

:evil:

If you're ever stuck on factoring a binomial you can always resort to the quadratic formula. It's obviously not the best method to use normally but can save you on a test. For this one:

-4a +- sqrt(16a^2 - 16a^2 + 4b^2) / 2
(-4a +- 2b)/2
-2a +- b
so your roots are -2a + b and -2a - b so your factors are (x + 2a + b)(x + 2a -b)
User avatar
Ikerous
Light Master
 
Posts: 977
Joined: Mon Dec 04, 2006 8:02 am
Location: California

Postby JustcallmeDrago » Tue Nov 06, 2007 3:29 am

TSchultz wrote:x^2 + 4ax + 4a^2
(x+2a)^2


OMG Why did I think that was impossible!?!?! :oops: Well, thanks!

& Ike, thanks a lot for that tip. I'd probably heard that from my teacher, but why would anyone listen to them over one's forum pals? ;P
User avatar
JustcallmeDrago
Contest Veteran
Contest Veteran
 
Posts: 904
Joined: Sun Mar 25, 2007 6:19 pm
Location: Earth

Postby JustcallmeDrago » Tue Nov 06, 2007 4:56 am

Solve by completing the square: (Teacher says answers need to be exact)

OK NOW SKIP TO BOTTOM.


2x^2 - 5x - 4 = 0

A = 2
B = -5
C = -4

Divide by A.

x^2 - (5/2)x - 2 = 0

B = -5/2

Rewrite as x^2 + bx on left side (basically move C to other side.)
x^2 - (5/2)x = 2

Add (B/2)^2 to each side.

x^2 - (5/2)x + (5/4)^2 = 2 + (5/4)^2
x^2 - (5/2)x + (5/4)^2 = 2 + 25/16
x^2 - (5/2)x + (5/4)^2 = 32/16 + 25/16
x^2 - (5/2)x + (5/4)^2 = 57/16
x^2 - (5/2)x + 25/16 = 57/16

Make left side into binomial.

(x - 5/4)^2 = 57/16

Square root the entire thing.

x - 5/4 = +- sqrt(57)/4

x = 5/4 +- sqrt(57)/4

5/4 + sqrt(57)/4
1.25 + ~7.55 / 4
1.25 + 1.8875

One of the answers is ~3.1375

I thought I did it right, but when I plug in 3.1375 into 2x^2 - 5x - 4 = 0

2(3.1375)^2 - 5(3.1375) - 4 = 0
2(9.84390625) - 15.6875 - 4 = 0
19.6878125 - 15.6875 - 4 = 0
4.0003125 - 4 = 0
0.0003125 ~= 0

Close enough.

Is the "exact" way to write the answer:

5/4 - sqrt(57)/4 & 5/4 + sqrt(57)/4

Or do I have to simplify?


Hey, look at me answering my own question!

5/4 - sqrt(57)/4
sqrt(25)/4 - sqrt(57)/4
sqrt(25 - 57)/4
sqrt(-32)/4
4i * sqrt(2) / 4

i * sqrt(2)

and

5/4 + sqrt(57)/4
sqrt(25)/4 + sqrt(57)/4
sqrt(25 + 57)/4

sqrt(82)/4
User avatar
JustcallmeDrago
Contest Veteran
Contest Veteran
 
Posts: 904
Joined: Sun Mar 25, 2007 6:19 pm
Location: Earth

Postby TSchultz » Tue Nov 06, 2007 5:17 am

sqrt(25)/4 - sqrt(57)/4
sqrt(25 - 57)/4

Square roots don't work that way.
Just leave it as (5+-Root(57))/4
User avatar
TSchultz
Contest Veteran
Contest Veteran
 
Posts: 508
Joined: Sat Jul 14, 2007 6:54 pm

Postby NickyNick » Tue Nov 06, 2007 3:12 pm

Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?
AR & W:A forever
User avatar
NickyNick
Champion of Light
Champion of Light
 
Posts: 1330
Joined: Sat Dec 30, 2006 10:43 pm
Location: Ukraine - Kharkov

Postby JustcallmeDrago » Tue Nov 06, 2007 7:11 pm

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?


-.- shut up. I actually never pay attention in class.
User avatar
JustcallmeDrago
Contest Veteran
Contest Veteran
 
Posts: 904
Joined: Sun Mar 25, 2007 6:19 pm
Location: Earth

Postby NickyNick » Tue Nov 06, 2007 8:25 pm

JustcallmeDrago wrote:
NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?


-.- shut up. I actually never pay attention in class.

Sorry, didn't want to offend you! Just really being very surprised.
In fact, math is very important subject, because it helps to involve logic and thinking.
AR & W:A forever
User avatar
NickyNick
Champion of Light
Champion of Light
 
Posts: 1330
Joined: Sat Dec 30, 2006 10:43 pm
Location: Ukraine - Kharkov

Postby JustcallmeDrago » Tue Nov 06, 2007 11:33 pm

NickyNick wrote:
JustcallmeDrago wrote:
NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?


-.- shut up. I actually never pay attention in class.

Sorry, didn't want to offend you! Just really being very surprised.
In fact, math is very important subject, because it helps to involve logic and thinking.


Whoops, sorry, I meant to say "-.- shut up. :P ". I am not offended.

Yeah, my schooling is strange because my math is the lowest level of all my classes, with English being my hardest and most advanced class, although I am best at math and worst at English.

What emphasis is put on English, ... or the equivalent where you live?
User avatar
JustcallmeDrago
Contest Veteran
Contest Veteran
 
Posts: 904
Joined: Sun Mar 25, 2007 6:19 pm
Location: Earth

Postby TSchultz » Tue Nov 06, 2007 11:53 pm

NickyNick wrote:Omg. These tasks are so easy... I'm very surprised that you have problems with them. Here 12-year-old kids solve such tasks in 2 minutes :? :?

Damn. Kids do Precalc at 12?
Damn. That means they'll have done Multivariable Calc by 14.
I thought I was ahead in math, but apparently I'm barely above average in Russia.
User avatar
TSchultz
Contest Veteran
Contest Veteran
 
Posts: 508
Joined: Sat Jul 14, 2007 6:54 pm

Postby NickyNick » Wed Nov 07, 2007 12:04 am

TSchultz wrote:Damn. Kids do Precalc at 12?
Damn. That means they'll have done Multivariable Calc by 14.
I thought I was ahead in math, but apparently I'm barely above average in Russia.

In Ukraine :wink:
In fact, I'm studying in physical-mathematical lyceum, one of the best in the whole country. Maybe, guys in ordinary schools are not so good in math, but the school programs for us and them are similar. It means that they study all this stuff in 12 too.
AR & W:A forever
User avatar
NickyNick
Champion of Light
Champion of Light
 
Posts: 1330
Joined: Sat Dec 30, 2006 10:43 pm
Location: Ukraine - Kharkov

Postby TSchultz » Wed Nov 07, 2007 1:01 am

NickyNick wrote:In Ukraine :wink:
In fact, I'm studying in physical-mathematical lyceum, one of the best in the whole country. Maybe, guys in ordinary schools are not so good in math, but the school programs for us and them are similar. It means that they study all this stuff in 12 too.

Ah! sorry.
I'm 4 grades ahead of people in my class, and they are all 1/2 years ahead of where kids normally are.
So Kids in Ukraine 5/6 years ahead of in the USA? That's scary.
User avatar
TSchultz
Contest Veteran
Contest Veteran
 
Posts: 508
Joined: Sat Jul 14, 2007 6:54 pm

Postby Nishimaster » Mon Nov 12, 2007 5:42 pm

How do I continue completing the square from y=3(x - 9)^2 - 108?

XD

I really suck at maths lol
Arrive, arise to your new world as this one dies. Forever death will embrace everything.
Nishimaster
Contest Winner
Contest Winner
 
Posts: 181
Joined: Wed Sep 20, 2006 1:07 pm
Location: Dewsbury, England

Postby NickyNick » Mon Nov 12, 2007 6:28 pm

y = 3(x-9)^2 - 108 = 3((x-9)^2 - 36) = 3((x-9)^2 - 6^2) = 3(x-15)(x-3)
AR & W:A forever
User avatar
NickyNick
Champion of Light
Champion of Light
 
Posts: 1330
Joined: Sat Dec 30, 2006 10:43 pm
Location: Ukraine - Kharkov

Postby Nishimaster » Mon Nov 12, 2007 6:50 pm

I worked it out just before you posted lol

how about this

when X^3 + pX^2 + p^2x - 36 is divided by x-3 the remainder is 21. Find a possible value of P.
Arrive, arise to your new world as this one dies. Forever death will embrace everything.
Nishimaster
Contest Winner
Contest Winner
 
Posts: 181
Joined: Wed Sep 20, 2006 1:07 pm
Location: Dewsbury, England

Postby Ikerous » Mon Nov 12, 2007 7:49 pm

Nishimaster wrote:I worked it out just before you posted lol

how about this

when X^3 + pX^2 + p^2x - 36 is divided by x-3 the remainder is 21. Find a possible value of P.

Do long division and you get a remainder of 3[3(p+3) + p^2] - 36 = 21

Solve for p and you get -5 and 2
User avatar
Ikerous
Light Master
 
Posts: 977
Joined: Mon Dec 04, 2006 8:02 am
Location: California

Previous

Return to Off Topic

Who is online

Users browsing this forum: No registered users and 5 guests

cron