 Algebra Marathon  

Author  Message 

skittles School Math Nerd
Number of posts : 40 Age : 23 Location : Lost Registration date : 20080813
 Subject: An Algebra Problem Wed Aug 13, 2008 6:47 pm  
 Let a and b be the roots of the equation x^2mx+2=0. Suppose that a+(1/b) and b+(1/a) are the roots of the equation x^2px+q=0. What is q? 

 
jellymuffins Starting Member
Number of posts : 14 Registration date : 20080813
 Subject: Re: Algebra Marathon Thu 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. =) 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 22 Location : Pleasanton, CA Registration date : 20080813
 Subject: Algebra Marathon Wed 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? 

 
johnnybeard New Member
Number of posts : 1 Registration date : 20080821
 Subject: Re: Algebra Marathon Thu Aug 21, 2008 10:05 am  
 All right man, that's not nice.
Anyway:
In 13 days, MY beard will be 49 inches long. 493=46. Multiply by 6 to get 276 dollars. I would never pay that much for a beard cut. 

 
isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: Re: Algebra Marathon Thu 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. 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 22 Location : Pleasanton, CA Registration date : 20080813
 Subject: Re: Algebra Marathon Thu 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


 
herefishyfishy1 Developer
Number of posts : 36 Age : 23 Location : An insignificant little bluegreen planet 93 million miles from the sun Sol. Registration date : 20080816
 Subject: Re: Algebra Marathon Thu 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 4x^{7}+7x^{6}2x^{5}+x^{3}8x^{2}8x+2? 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 22 Location : Pleasanton, CA Registration date : 20080813
 Subject: Re: Algebra Marathon Thu 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


 
isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: Re: Algebra Marathon Fri Aug 22, 2008 8:43 am  
 3*5 = 15. can run 15 mph. He ran 24000 miles. How many days was he running? 

 
Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: Re: Algebra Marathon Fri 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


 
FantasyLover Starting Member
Number of posts : 8 Location : Fantasy World Registration date : 20080824
 Subject: Re: Algebra Marathon Mon 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? 

 
isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: Re: Algebra Marathon Tue 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? 

 
Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: Re: Algebra Marathon Tue Aug 26, 2008 11:23 pm  
 Is profit/apple. Is how many apples she needs. Find the polynomial that has the roots that are recriprocals of the roots of: _________________ ~Dojo


 
ternary0210 School Math Nerd
Number of posts : 41 Age : 21 Registration date : 20080817
 Subject: Re: Algebra Marathon Mon Sep 08, 2008 4:55 pm  
 x^2+6x9 Find (sqrt(12+sqrt(12+sqrt(12... Replace 12 with... a)2 b)6 c)20 d)30 Dojo 

 
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 Subject: Re: Algebra Marathon  
 

 
 Algebra Marathon  
