The Math Forum

For anyone with a love of math
 
HomeHome  CalendarCalendar  GalleryGallery  FAQFAQ  SearchSearch  MemberlistMemberlist  UsergroupsUsergroups  RegisterRegister  Log in  

Share
 

 Algebra Marathon

Go down 
AuthorMessage
skittles
School Math Nerd
School Math Nerd
skittles

Number of posts : 40
Age : 24
Location : Lost
Registration date : 2008-08-13

Algebra Marathon Empty
PostSubject: An Algebra Problem   Algebra Marathon EmptyWed Aug 13, 2008 6:47 pm

Let a and b be the roots of the equation x^2-mx+2=0. Suppose that a+(1/b) and b+(1/a) are the roots of the equation x^2-px+q=0. What is q?
Back to top Go down
View user profile
jellymuffins
Starting Member
Starting Member


Number of posts : 14
Registration date : 2008-08-13

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 14, 2008 11:01 am

Well from vieta

q = (a + 1/b)(b + 1/a) = ab + 1 + 1 + 1/ab

And again by vieta we know that ab = 2 from x^2 - mx + 2 = 0

2 + 1 + 1 + 1/2 = 4 1/2

Nice problem! =)


Edit: Try to find p. =)
Back to top Go down
View user profile
AIME15
Hardcore TMF user
Hardcore TMF user
AIME15

Number of posts : 163
Age : 22
Location : Pleasanton, CA
Registration date : 2008-08-13

Algebra Marathon Empty
PostSubject: Algebra Marathon   Algebra Marathon EmptyWed Aug 20, 2008 1:54 pm

Would anyone like to have an algebra marathon?

If so: Normal marathon rules. Remember to POST A PROBLEM AFTER YOU SOLVE ONE.

First problem: Johnny's Beard is very long, in fact, it's 3 feet long. It costs 6 dollars per inch cut, and Johnny wants his beard cut in 13 days. His beard grows one inch every day. How much will it cost him to cut his beard to just 3 inches long?
Back to top Go down
View user profile
johnnybeard
New Member
New Member


Number of posts : 1
Registration date : 2008-08-21

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 21, 2008 10:05 am

All right man, that's not nice.

Anyway:

In 13 days, MY beard will be 49 inches long. 49-3=46. Multiply by 6 to get 276 dollars. I would never pay that much for a beard cut.
Back to top Go down
View user profile
isabella2296
Admin
Admin


Number of posts : 45
Location : You'd really like to know, wouldn't you?
Registration date : 2008-08-16

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 21, 2008 1:05 pm

AIME15 wrote:


If so: Normal marathon rules. Remember to POST A PROBLEM AFTER YOU SOLVE ONE.

Please read directions, Johnny.
Back to top Go down
View user profile
AIME15
Hardcore TMF user
Hardcore TMF user
AIME15

Number of posts : 163
Age : 22
Location : Pleasanton, CA
Registration date : 2008-08-13

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 21, 2008 1:57 pm

Yes johnny, it's a very important part of life, reading directions. Anyway:

When Maya divides her favorite number by 11, she gets a remainder of 4.What will the remainder be if she multiplies her favorite number by 4 and then divides by 11?

_________________
-AIME15, Moderator of Algebra Forum
Back to top Go down
View user profile
herefishyfishy1
Developer
Developer


Number of posts : 36
Age : 24
Location : An insignificant little blue-green planet 93 million miles from the sun Sol.
Registration date : 2008-08-16

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 21, 2008 3:04 pm

Well, if we call the number a, then a=4 (mod 11). If we multiply both sides by 4, we get 4a=16 (mod 11). 16=5 (mod 11). Therefore, 4a=5 (mod 11). And therefore, the answer is 5.

What is the product of the roots of 4x7+7x6-2x5+x3-8x2-8x+2?
Back to top Go down
View user profile
AIME15
Hardcore TMF user
Hardcore TMF user
AIME15

Number of posts : 163
Age : 22
Location : Pleasanton, CA
Registration date : 2008-08-13

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyThu Aug 21, 2008 3:29 pm

Using vieta: it's -2/4=-1/2, right?

New Problem: How many integer divisors does 5625 have, given 5625=3^2*5^4?

_________________
-AIME15, Moderator of Algebra Forum
Back to top Go down
View user profile
isabella2296
Admin
Admin


Number of posts : 45
Location : You'd really like to know, wouldn't you?
Registration date : 2008-08-16

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyFri Aug 22, 2008 8:43 am

3*5 = 15.

rendeer can run 15 mph. He ran 24000 miles. How many days was he running?
Back to top Go down
View user profile
Dojo
Admin
Admin
Dojo

Number of posts : 154
Location : Probably somewhere near a computer
Registration date : 2008-08-12

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyFri Aug 22, 2008 9:52 am

24000/15=1600
1600/24=66 2/3

(Heres a sad question I'm gonna make up)
Currently, Joe is half the age of sally.
In 24 years, Sally will be 1 and 1/3 Joe's age.
How old is Joe?

_________________
~Dojo
Back to top Go down
View user profile http://themathforum.forumotion.com
FantasyLover
Starting Member
Starting Member
FantasyLover

Number of posts : 8
Location : Fantasy World
Registration date : 2008-08-24

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyMon Aug 25, 2008 11:42 am

J=1/2 S
S+24=4/3 (J+24)

S+24=4/3J+32

2J+24=4/3J+32, 2/3J=8, J=12

answer : 12



Fantasy runs 12 miles in 3 hours. How many miles would he run in 4 hours?
Back to top Go down
View user profile
isabella2296
Admin
Admin


Number of posts : 45
Location : You'd really like to know, wouldn't you?
Registration date : 2008-08-16

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyTue Aug 26, 2008 11:39 am

-sigh-

Algebra doesn't mean amazingly easy peasy.

12/3 = x/4

x = 16

Fantasy buys 60 apples for 5 dollars, and then sells them for an average of 10 cents per apple. How many apples does he have to buy and sell to get a total profit of at least 200 dollars?
Back to top Go down
View user profile
Dojo
Admin
Admin
Dojo

Number of posts : 154
Location : Probably somewhere near a computer
Registration date : 2008-08-12

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyTue Aug 26, 2008 11:23 pm

Algebra Marathon Bb5a939d66aa4320b535049fd016f4259129a0a8

Is profit/apple.

Algebra Marathon 3e888fae7bc31eaa5087a60bb183eb06daa03018

Is how many apples she needs. Nervous


Find the polynomial that has the roots that are recriprocals of the roots of:
Algebra Marathon 6891ed90a8388e958ee721c93678711b490d3b96

_________________
~Dojo
Back to top Go down
View user profile http://themathforum.forumotion.com
ternary0210
School Math Nerd
School Math Nerd


Number of posts : 41
Age : 21
Registration date : 2008-08-17

Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon EmptyMon Sep 08, 2008 4:55 pm

x^2+6x-9

Find (sqrt(12+sqrt(12+sqrt(12...
Replace 12 with...
a)2
b)6
c)20
d)30
I love you Dojo
Back to top Go down
View user profile
Sponsored content




Algebra Marathon Empty
PostSubject: Re: Algebra Marathon   Algebra Marathon Empty

Back to top Go down
 
Algebra Marathon
Back to top 
Page 1 of 1
 Similar topics
-
» Math Problems and Giving Up

Permissions in this forum:You cannot reply to topics in this forum
The Math Forum :: Middle School Topics :: Problem Solving :: Marathons-
Jump to: