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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

Find the condition that the roots of the equation

are in the ratioMy 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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,379

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

Let the roots be and . Thus

Eliminating

givesas the required condition.

Test:

have roots in the ratio .*Last edited by scientia (2013-02-27 12:24:16)*

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

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

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The essence of mathematics lies in its freedom - Georg Cantor

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,379

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

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

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The essence of mathematics lies in its freedom - Georg Cantor

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,379

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

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 ratioSolution :

Let

and be the two roots of the equationNow,

---Eq 1and

---Eq 2From Eq 1 we have ,

or ,

or ,

--- By Eq2or ,

which is the required condition

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

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The essence of mathematics lies in its freedom - Georg Cantor

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,379

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)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

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 dont understand the question clearly, posting the solution doesnt means you know about it, their are many books where you will find this question and its solution.

Now the main thing, please please please please never ever try to help me again in future ,just stick with your bed and have good dreams...

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The essence of mathematics lies in its freedom - Georg Cantor

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,379

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)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

**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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**debjit625****Member**- Registered: 2012-07-23
- Posts: 91

@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.

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The essence of mathematics lies in its freedom - Georg Cantor

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'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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