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Algebra
Mirka's Avatar
Mirka
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Joined: 13 Aug 2008
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28 Mar 2009 07:40:50 IST
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Try this Q -
None

 

 

Consider the equation     

 

What r the conditions on alpha (  ) such that eqn has :

 

 

 

(A)   no real roots ?

 

(B)   one real root ?

 

(C)   2 +ve and 1 –ve real root ?

 

(D)   3 +ve roots ?

 

 

 

Answers given were :

 

(A) 

 

(B) 

 

(C) 

 

(D) 

 

 

 

 

I have no clue how to solve such Qsns !  

 

 

 


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R Srivatsan
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Joined: 30 Oct 2008
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28 Mar 2009 13:07:29 IST
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Try this Q -
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R Srivatsan
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28 Mar 2009 13:08:48 IST
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this Q can be solved by finding the range of the function on LHS
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R Srivatsan
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28 Mar 2009 13:11:25 IST
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behaviour of function is like this;it decreases for x<-2,not defined for -2
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R Srivatsan
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28 Mar 2009 13:13:07 IST
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AIR 538 Asish
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2 Apr 2009 08:35:21 IST
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For (A) we know that e^(1/x)>0 and (x^2+2x)^1/2 >0 so @ must be >0 so if @ <0 then there will be no real roots for the equation..
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Soumik
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2 Apr 2009 13:52:57 IST
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The full soln is there in Mirka's nudgebook.
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Shreya
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2 Apr 2009 14:27:12 IST
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hey i didnt find the soln, can u post it here plz
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neeharika
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Joined: 31 Mar 2009
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3 Apr 2009 09:02:23 IST
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hey pls post de ans for me also im not getting correct ans
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Mirka's Avatar

Mirka
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3 Apr 2009 09:45:36 IST
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 @  soumik : I AM SO SORRY 4 having deleted all my nudges by that time ….

 

 

 

 

See, lets consider the function 

 

Obviously, since e power 1/x and sqrt ( x2 + 2x ) is both +ve,

 

Alpha shud be + ve

 

Hence, fr option A … no real root,

 

Alpha < 0

 

 

 

Lets try drawing d graph …

See dat graph is defined only at points where x <=  -2 and x > 0

 

Differentiating gives

 

 

 f ’ (x) = 0 at x = root(2)

 

so, extrema of d graph occurs at that point …

 

Here I have drawn an approximate graph !!

 

 

wait .... i need an approval ...

 
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Soumik
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3 Apr 2009 20:18:37 IST
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Approved Cool (speak)..............
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