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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!!!!!!!!!!!!!

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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
Re: Math : Algebra 101   [#permalink] 07 Jan 2015, 13:17

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