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#1 2013-02-27 05:34:22

debjit625
Member
Registered: 2012-07-23
Posts: 101

Find the condition that the roots of the equation

are in the ratio

My problem is that I didnt understood this question i.e.. the language ,what condition its talking about... the two roots may be ma and na that will be in the ratio but what I have to show/do here.

Thanks:)

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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#2 2013-02-27 07:03:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

I am getting,

with r1 being an arbitrary root.

Last edited by bobbym (2013-02-27 07:03:44)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2013-02-27 12:19:00

scientia
Member
Registered: 2009-11-13
Posts: 224

Let the roots be
and
. Thus

Eliminating

gives

as the required condition.

Test:

have roots in the ratio
.

Last edited by scientia (2013-02-27 12:24:16)

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#4 2013-02-28 04:06:12

debjit625
Member
Registered: 2012-07-23
Posts: 101

Ok I think you guys didn't understood what I was asking for...
I want to know what the question is asking for ,what condition ?

As bobbym showed I think the question is asking about the values of the coefficients which will make the roots of the equation in m:n ratio.Am I right ? if I am not please help me to understand

Thanks bobbym and scientia

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#5 2013-02-28 04:10:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

The values of the coefficients are in post #2. They are a,b and c, but you will also have specify one value as one root.

Last edited by bobbym (2013-02-28 04:12:51)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2013-02-28 04:19:15

debjit625
Member
Registered: 2012-07-23
Posts: 101

The values of the coefficients are in post #1

I have seen that...
I am just confused what the question is asking for...

In the book the process is a bit different but the required condition is given like scientia did

But still I am confused... I think I have to think about some more time...

Thanks

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#7 2013-02-28 04:26:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

You will have to wait until she comes back in for an explanation. I never see anything the way them dudes that write them there books do.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2013-02-28 04:56:16

debjit625
Member
Registered: 2012-07-23
Posts: 101

I had also never seen this kind of stuff earlier...

Well in the book its done like this...

Find the condition that the roots of the equation

are in the ratio

Solution :

Let

and
be the two roots of the equation

Now,

---Eq 1

and

---Eq 2

From Eq 1 we have ,

or ,

or ,

--- By Eq2

or ,

which is the required condition

Last edited by debjit625 (2013-02-28 05:09:08)

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#9 2013-02-28 06:28:56

scientia
Member
Registered: 2009-11-13
Posts: 224

What the bleep is wrong? The question asks for the condition under which certain things hold. I worked out and gave the condition. Just what are you not happy with?

debjit625 wrote:

Ok I think you guys didn't understood what I was asking for...
I want to know what the question is asking for ,what condition ?

Look. You asked a question. I took the time to help you with it. It was late, I could have gone to bed, but I stayed up to help you. Is this the gratitude I get in return?

Maybe what you don't understand is not the question but the English language?

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#10 2013-02-28 08:02:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi scientia;

I do not think he meant it that way, also he was talking about my post and it probably came out looking that he meant you and I.

Since you came up with the exact answer he required it was just a misunderstanding. Very good answer by the way.

Last edited by bobbym (2013-02-28 08:05:07)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2013-02-28 19:03:44

debjit625
Member
Registered: 2012-07-23
Posts: 101

Is this the gratitude I get in return?

scientia ,if you can read English and understand it then look at post #4 ,I appreciated your work ,I thanked you...

Doing the sum is nothing its simple....

Maybe what you don't understand is not the question but the English language?

Yes, in general I speak English and understand it properly, but this question is not very much clear and I think bobbym also agreed with me on #7

My main question on post #1 was about clarification of the question elaborately ,I was not asking about the solution.

If somebody ask you --- What the question is asking for ? Find the roots of equation

.
And you just solve the equation ,that what you did in my case ,will not answer his/her question, you need to explain him/her what does the roots means in an quadratic equation.

You knew what I asked for... but you yourself dont understand the question clearly, posting the solution doesnt means you know about it, their are many books where  you will find this question and its solution.

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#12 2013-02-28 20:53:53

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

I am hoping that there is no more hard feelings over this question. You have both vented your feelings and hopefully it is over.

Please no more retaliation. Let's just forget it happened.

Last edited by bobbym (2013-02-28 22:13:38)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2013-03-01 02:42:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
Website

Debjit, are you a bengali?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#14 2013-03-01 08:18:52

scientia
Member
Registered: 2009-11-13
Posts: 224

debjit625, I'm sorry for my bad-tempered post above. I suppose I had had a bad day and somehow let it spill over onto the forum. It was totally wrong of me and I apologize.

Anyway, "condition" simply means something that has to be fulfilled in order for a given statement to be true. For example, suppose the question was: "What's the condition under which the quadratic equation
,
, has no real roots?" Then the condition would be:
. In order for the statement "
,
, has no real roots" to be true, the condition
has to be fulfilled.

In this particular question, the statement is "

(
) has roots in the ratio
". In order for this to be true, we must have
. This is the condition that has to be fulfilled in order for the given statement to be true.

Last edited by scientia (2013-03-01 08:20:03)

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#15 2013-03-01 21:35:36

debjit625
Member
Registered: 2012-07-23
Posts: 101

@scientia I am sorry too, for being so rude
And sorry to everybody I could be a bit more polite...

@Agnishom, yes brother

And about the question, yes I have understood it ,its asking for the condition i.e.. a relation between the roots and the coefficients for which the roots will be in m:n ratio.

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#16 2013-03-01 22:48:10

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
Website