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quadratic equation

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by rupsk » Tue Sep 06, 2011 7:57 pm
If the roots of are equal, a(b-c)x*x + b(c-a)x + c(a-b)=0 then a,b,c are in ?

A. A.P

B. H.P

C. A.G.P

D. G.P

E. None



If the roots of the equation ax*x +bx +c =0 are the reciprocals of the roots of the equation px*x+ qx +r=0 then which of the following is true?

1. ab=pq
2. acqq= bbpr
3. ac=pr
4. bbac=qqpr
5. abbac=qqqpr
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by Anurag@Gurome » Tue Sep 06, 2011 8:27 pm
If the roots of are equal, a(b-c)x*x + b(c-a)x + c(a-b)=0 then a,b,c are in ?

A. A.P
B. H.P
C. A.G.P
D. G.P
E. None

It can be seen that for x = 1, a(b - c) + b(c - a) + c(a - b) = ab - ac + bc - ba + ca - bc = 0
Since the roots are equal, so c(a - b)/a(b - c) = 1
c(a - b) = a(b - c)
ac - bc = ab - ac
2ac = bc + ab
b = 2ac/(a + c)
So, a, b, c are in H.P.

The correct answer is B.
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by garima99 » Tue Sep 06, 2011 8:39 pm
rupsk wrote:If the roots of are equal, a(b-c)x*x + b(c-a)x + c(a-b)=0 then a,b,c are in ?

A. A.P

B. H.P

C. A.G.P

D. G.P

E. None

this would mean that the determinant is zero...[b(c-a)]^2 -4[a(b-c)][c(a-b)]=0



If the roots of the equation ax*x +bx +c =0 are the reciprocals of the roots of the equation px*x+ qx +r=0 then which of the following is true?
c/a*r/p=1
1. ab=pq
2. acqq= bbpr
3. ac=pr
4. bbac=qqpr
5. abbac=qqqpr
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by Ian Stewart » Tue Sep 06, 2011 10:17 pm
rupsk wrote:If the roots of are equal, a(b-c)x*x + b(c-a)x + c(a-b)=0 then a,b,c are in ?

A. A.P

B. H.P

C. A.G.P

D. G.P

E. None
I imagine many people reading this forum won't even know what 'H.P' or 'A.G.P.' even stand for. If you're preparing for the GMAT, you don't need to know; these are most definitely not GMAT questions.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by prashant.mishra » Wed Sep 07, 2011 1:18 am
Hi Anurag,

I do agree that when x is assumed as 1, we get an H.P. But the same won't be true for any other value of x. Lets assume x=2 then, 4a(b-c) + 2b(c-a) + c(a-b)=0

4ab - 4ac + 2bc - 2ab + ac - bc = 0
=> 2ab + bc = 3ac This is true for a=1, b=1, c=1 which is not an H.P.

Alternatively,
c(a-b)/a(b-c)=2*2

ac-bc= 4ab -4ac
=> 5ac=4ab+bc - again, this equation is true for a=1, b=1, c=1. and not for other values.

So how can we say that the three values are definitely in H.P. ? Pls clarify.
Anurag@Gurome wrote:If the roots of are equal, a(b-c)x*x + b(c-a)x + c(a-b)=0 then a,b,c are in ?

A. A.P
B. H.P
C. A.G.P
D. G.P
E. None

It can be seen that for x = 1, a(b - c) + b(c - a) + c(a - b) = ab - ac + bc - ba + ca - bc = 0
Since the roots are equal, so c(a - b)/a(b - c) = 1
c(a - b) = a(b - c)
ac - bc = ab - ac
2ac = bc + ab
b = 2ac/(a + c)
So, a, b, c are in H.P.

The correct answer is B.
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by saketk » Wed Sep 07, 2011 9:03 am
I don't think we need Harmonic Progression in GMAT.
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by prashant.mishra » Fri Sep 09, 2011 5:23 am
Hi Anurag,

I anticipate your response.. When we select other values of x (for eg. x=2) the same equation does not give an H.P. Please clarify on how we can convincingly say that a, b and c will be in H.P.

Thanks.

@ Saketk

This question may not be important for GMAT but how about adding value to your knowledge? :)
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by Brent@GMATPrepNow » Fri Sep 09, 2011 5:49 am
prashant.mishra wrote: This question may not be important for GMAT but how about adding value to your knowledge? :)
I'm in favor of people adding value to their knowledge, but it shouldn't be at the expense of people who want to focus solely on preparing for the GMAT.

If people want to post wildly-out-of-scope questions on this forum, so be it. However, these questions should be accompanied by a proviso that says something like "This question has nothing to do with the GMAT" so that people who are unfamiliar with the GMAT curriculum don't panic.

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by saketk » Fri Sep 09, 2011 6:10 am
prashant.mishra wrote:
@ Saketk

This question may not be important for GMAT but how about adding value to your knowledge? :)
Hey Prashant, I totally understand your point that extra knowledge is useful, but I agree with Brent's point as well. Why would I divulge from the track and do this question when I absolutely don't need to :)

just to clear - I know how to solve this question. This is not a difficult question for me only because I still remember, from my high school days, the methods to deal with progressions :).
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by rupsk » Fri Sep 09, 2011 6:38 am
Hi Everyone,

It seems my questions have created a lot of misunderstanding here, my intention were not to post any question which are not part of GMAT. This questions I got from website which have collection of test papers for GMAT. So if it is not part of GMAT then please do not waste your time on answering my questions as I got it earlier only that it is not part of GMAT.


Thanks
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by Brent@GMATPrepNow » Fri Sep 09, 2011 6:43 am
rupsk wrote:Hi Everyone,

It seems my questions have created a lot of misunderstanding here, my intention were not to post any question which are not part of GMAT. This questions I got from website which have collection of test papers for GMAT. So if it is not part of GMAT then please do not waste your time on answering my questions as I got it earlier only that it is not part of GMAT.
Thanks
Hi rupsk,

Thanks for clearing that up.

There are definitely a lot of out-of-scope GMAT resources circulating out there, and unless one has in-depth knowledge of the GMAT curriculum, it's easy to be led to believe that the questions are legitimate.

What was the source of the questions?

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by saketk » Fri Sep 09, 2011 8:33 am
Hi Brent -- This question is from Indian institute of technology Joint Entrance Examination i.e. (IIT JEE) . subjects tested are -- Math, Physics and Chemistry..

This exam is conducted in India for admission in Premier Engineering colleges in India, namely -- all IIT's (indian institute of technology) and IIIT's ( indian institute of information technology) ..

This exam is considered as the toughtest nut to crack and is one of the toughest exam for engineering in the world.


PS: My younger brother saw me typing here and told me that this one is from IIT exam :) .. I had to explain this question to him in the end :)

one more thing I came across is that Not only this question is not for GMAT, it is posted wrongly as well.

the question should look like -- " a(b-c)x^2+b(c-a)x+c(a-b)=0 "
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by Brent@GMATPrepNow » Fri Sep 09, 2011 8:37 am
saketk wrote:Hi Brent -- This question is from Indian institute of technology Joint Entrance Examination i.e. (IIT JEE) . subjects tested are -- Math, Physics and Chemistry..

This exam is conducted in India for admission in Premier Engineering colleges in India, namely -- all IIT's (indian institute of technology) and IIIT's ( indian institute of information technology) ..

This exam is considered as the toughtest nut to crack and is one of the toughest exam for engineering in the world.
I see.
I guess the question should be posted on the Beat The IIT JEE site then :-)

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by rupsk » Fri Sep 09, 2011 5:57 pm
ohh!!!! I know about IIT its the toughest one to crack...
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