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Algebra

New kid on the Block

 Joined: 17 Jan 2012 Post: 26
27 Mar 2012 22:19:25 IST
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Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

no. of real roots of eq (x^2+2x)^2 - (x+1)^2 - 55 = 0 is:a. 1b. 2c. 4d. none of these

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Blazing goIITian

Joined: 21 Mar 2012
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27 Mar 2012 22:30:52 IST
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Very gud It has two real roots given by -4,2..

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
27 Mar 2012 22:31:43 IST
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Pls pls pls dont forget to ht like if i am ryte

Blazing goIITian

Joined: 21 Mar 2012
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27 Mar 2012 22:51:01 IST
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Say na dude u r ryte

Blazing goIITian

Joined: 8 Sep 2011
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27 Mar 2012 22:51:56 IST
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how did u get the roots can u explain?

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
27 Mar 2012 23:00:40 IST
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Okzz if we expand it it wil bcoz biquadratic eq. Which would nearly imposible to solve so we apply a2-b2 in(x^2+2x)^2-(x+1)^2 we get (x^2+3x+1)(x^2+x-1)=55=11*5 now i first asume that x2+3x+1=11 i get x=2,-5 and x2+x-1=5 i get x=-3,2 so frm here we get one root as x=2 and similarly let x2+3x+1=5 and x2+x-1=11 frm them we get x=-4 so overall roots are x=2,-4

Blazing goIITian

Joined: 21 Mar 2012
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27 Mar 2012 23:01:05 IST
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Got it

Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
27 Mar 2012 23:01:46 IST
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Dont forget to like

Blazing goIITian

Joined: 8 Sep 2011
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27 Mar 2012 23:05:23 IST
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thanx.. smart huh..

Blazing goIITian

Joined: 21 Mar 2012
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27 Mar 2012 23:07:02 IST
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thank u lolzzzzzz.......

Blazing goIITian

Joined: 25 Jul 2011
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27 Mar 2012 23:21:53 IST
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$The answer for this question is 2 ,$

$(x^2+2x)^2 - (x+1)^2 - 55$

$\Leftrightarrow x^4+4x^3+3x^2-2x-56=0$

$\Leftrightarrow x(x^3+4x^2+3x-2)=56$

$The factors of 56 are: (2*28),(-2*-28),(-7*-8),(7*8),(4*14),(-4*-14)$

$2 and -4 only satisfies this equation$

$Therefore,the answer for this question is option (b) that is 2$

$Like my answer if it was helpful :) :) :) :) :)$

New kid on the Block

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29 Mar 2012 16:43:03 IST
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sorry,for replying late.by d way ,it has only 1 real root.ques is from 11th r.d.sharma mcq

Blazing goIITian

Joined: 25 Jul 2011
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29 Mar 2012 16:46:44 IST
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Sorry...All my steps r right.....Only 2 satisifies not -4....rest all is crect....Yes the ans is 1 only.....

New kid on the Block

Joined: 17 Jan 2012
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29 Mar 2012 16:49:59 IST
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pls let me know if u get d right ans.by d way many ans of mcq are wrong.

New kid on the Block

Joined: 17 Jan 2012
Posts: 26
29 Mar 2012 16:51:50 IST
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k thanxxx.....

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
29 Mar 2012 16:52:29 IST
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Blazing goIITian

Joined: 21 Mar 2012
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29 Mar 2012 18:01:43 IST
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Hey sathyaram -4 and 2 both satisfy then the eq. Then how cn u say the root is only one

Blazing goIITian

Joined: 25 Jul 2011
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29 Mar 2012 18:32:02 IST
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Ya...ur right dude....Misconception...

Blazing goIITian

Joined: 21 Mar 2012
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29 Mar 2012 18:38:12 IST
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Then pls like me

Blazing goIITian

Joined: 25 Jul 2011
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29 Mar 2012 18:41:19 IST
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