Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

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

Quadratic Equation

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,745

Re: Quadratic Equation

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

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

Re: Quadratic Equation

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)

Offline

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

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

Re: Quadratic Equation

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,745

Re: Quadratic Equation

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

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

Re: Quadratic Equation

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,745

Re: Quadratic Equation

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

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

Re: Quadratic Equation

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

Offline

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

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

Re: Quadratic Equation

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? mad


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? swear

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,745

Re: Quadratic Equation

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

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

Re: Quadratic Equation

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.

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...


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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,745

Re: Quadratic Equation

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,993
Website

Re: Quadratic Equation

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

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

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

Re: Quadratic Equation

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. sad


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)

Offline

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

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

Re: Quadratic Equation

@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

Offline

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,993
Website

Re: Quadratic Equation

smile


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

Board footer

Powered by FluxBB