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Math : Algebra 101

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Re: Math : Algebra 101 [#permalink] New post 29 Jan 2013, 05:47
VeritasPrepKarishma wrote:
Archit143 wrote:
Need Help!!! Urgent

What is the difference between the solution of below problems, Is there any difference in the approach:-
1. X^3 > X

soln: -1<X<0 or X>1

If we follow the above principle for solving than the answer to below equation must be:

2. a^3< a^2 + 2a

-1<a<0 or a>2

but the answer as per MGMAt quant book is
0<a<2 or a<-1

Pls help me in getting the right concept.........


Responding to a pm:

2. a^3< a^2 + 2a

a^3 - a^2 - 2a < 0
a(a - 2)(a + 1) < 0

......-1.....0............2.......

Since you want the expression to be negative, the required range is a < -1 or 0 < a < 2 (Notice the sign in the original inequality. It is less than)

The range you have written: -1<a<0 or a>2 is for the expression to be positive.

Check out these posts for further clarification:

http://www.veritasprep.com/blog/2012/06 ... e-factors/
http://www.veritasprep.com/blog/2012/07 ... ns-part-i/
http://www.veritasprep.com/blog/2012/07 ... s-part-ii/
http://www.veritasprep.com/blog/2012/07 ... qualities/


Karishma

You are no less than Ron ...I would rate you above them in Maths
I mean what great explanations.......
can you fw the links of your blog on MODULUS, various type of questions.....
Thanks a trillion....I am sure i have added atleast 1 point to my maths score.......

Was it so simple!!!!!!!!I am thinking now!!!!!!!!!!!!!!!!!!!!
Waiting for links on modulus!!!!!!!!!!!!!

Archit
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Re: Math : Algebra 101 [#permalink] New post 10 Jul 2013, 23:06
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Re: Math : Algebra 101 [#permalink] New post 23 Oct 2013, 06:17
Thank you for the book, it is a very useful one. I have a question on Solving equations of degree 2 : QUADRATIC part.
"The sum is -11 and the product is 30. So numbers are -5,-6". I think there is a typo: the sum is 11 (=b), not -11 as far as the solutions are x1=-5, and x2=-6 (we have 2 binomials (x+5) and (x+6). Please correct if I am wrong.
Thanks again.
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Re: Math : Algebra 101 [#permalink] New post 24 Oct 2013, 01:26
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marvas wrote:
Thank you for the book, it is a very useful one. I have a question on Solving equations of degree 2 : QUADRATIC part.
"The sum is -11 and the product is 30. So numbers are -5,-6". I think there is a typo: the sum is 11 (=b), not -11 as far as the solutions are x1=-5, and x2=-6 (we have 2 binomials (x+5) and (x+6). Please correct if I am wrong.
Thanks again.


The sum of the roots is (-5) + (-6) = -11, which is -b/a=-(11/1)=-11.

Hope it's clear.
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Re: Math : Algebra 101 [#permalink] New post 07 Jan 2015, 13:17
this post has been really helpful. Thank you
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Re: Math : Algebra 101 [#permalink] New post 29 Jun 2015, 15:05
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shrouded1 wrote:
Eg. \(x^6 -3x^3 + 2 = 0\)
Here let \(y=x^3\)
\(y^2-3y+2=0\)
\((y-2)(y-1)=0\)

So the solution is y=1,2 or x^3=1,2 or x=1,cube_root(3)


Hi,

First of all, numerous thanks for all the work on this forum, it is so helpful.

I was going through the Math book and noticed a typo on the solution above. Shouldn't x = 1 & cube_root(2) ? Not a big deal, but always worth mentioning!
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Re: Math : Algebra 101 [#permalink] New post 30 Jun 2015, 03:09
Expert's post
RCM wrote:
shrouded1 wrote:
Eg. \(x^6 -3x^3 + 2 = 0\)
Here let \(y=x^3\)
\(y^2-3y+2=0\)
\((y-2)(y-1)=0\)

So the solution is y=1,2 or x^3=1,2 or x=1,cube_root(3)


Hi,

First of all, numerous thanks for all the work on this forum, it is so helpful.

I was going through the Math book and noticed a typo on the solution above. Shouldn't x = 1 & cube_root(2) ? Not a big deal, but always worth mentioning!


Edited the typo. Thank you!
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Math : Algebra 101   [#permalink] 30 Jun 2015, 03:09

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