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Quadratic Equation
by Total Gadha - Saturday, 5 July 2008, 04:21 AM
  cat 2008 cat 2009 mba 2008 quadratic euqationI have not written for a while for my CAT 2010 students, not because I didn't want to but because the explosive growth of and TathaGat kept me busy in multidimensional roles. Gone are the long evening walks, leisurely problem-solving sessions and book readings. Now my time is spent in hurried classroom sessions, editing worksheets, answering incessant phone calls, and managing a rapidly-growing team. The pleasures and pains of entrepreneurship are numerous. Not that I am complaining. It feels good to see that an idea which was once a passing thought has blossomed into something real. It is heartening to see that you can do a lot of good in this world. was once a thought. Now it is a reality. It would give rise to more realities. Tomorrow, there would be something better than There would be better thoughts. And in the end, it would be the students who would benefit the most by the new realities. It is reason enough to rejoice, pain of entrepreneurship notwithstanding.

One more CAT is approaching fast. There is already a tightening in my stomach, a lump in my throat. If I could have my wish, I would want all my students and TGites to clear CAT. But this is not possible, and in the end, life wouldn’t be interesting without a good mix of victories and defeats. No matter what happens on the D-day, I hope that the students don’t stop learning at least. Amen! So here is it ladies and gentlemen, a fruit of painful labour. smile

cat 2008 cat 2009 quadratic equation

quadratic equation 2

quadratic equation 3
quadratic equation 4
quadratic equation 5
quadratic equation 6

I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.


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Re: Quadratic Equation
by Amit A - Saturday, 5 July 2008, 12:53 PM

Hello Sir ,

Thanks a lot for yet another enlightining article. I just wanted to drive your attention to one minor mistake in one of the examples listed in this article.                                            The First illustration in the section (Completing the Square) , the equation x2 - 10x - 6 =0 should be having minimum value as -31 (and not -25).

Please let me know if I m wrong.

And please keep posting such informative articles because your forum is the only one I (and many others) trust most.





Re: Quadratic Equation
by y v - Saturday, 5 July 2008, 03:35 PM
  TG sir...You have forgotten to add -6..So the answer is -31 as Amit has pointed out...
Article was very useful sir...
Please post an article on time and work
Re: Quadratic Equation
by ATOM ANT - Saturday, 5 July 2008, 03:51 PM
  TG sir,

I have few doubts.

1.Can you give me an example of a parabola that touches only x-axis?

2.You have given three different curves for the quadratic equation with a>0 and a<0... what is the form of equation where the curve do not touch x-axis...
is it like y = x2 + k..

3.Are parabolas neccessarily symmetrical ?

and I would like to add a point to your lesson.
For any quadratic equation of the form ax2 + bx + c = 0

for every single change of sign there is a positive root.

eg: x2 + 5x + 6 = 0 roots = -2,-3

x2 -5x - 6 = 0 roots = -1,6

x2 -5x + 6 = 0 roots = 2,3

Thanks a lot for the lesson.. Btw where should I post my doubts on questions from Copycat-1... Unfortunately my previous post was deleted.

Re: Quadratic Equation
by tinu doshi - Saturday, 5 July 2008, 08:56 PM
  hello sir,
excellence is the word for u!!!!!!!!!!!
Re: Quadratic Equation
by amit kumar - Sunday, 6 July 2008, 07:12 PM

hi tg sir,

               very nice article.keep posting these as they are really usefull

Re: Quadratic Equation
by Rajakannan R - Tuesday, 8 July 2008, 12:06 PM

Hello  sir,

For the problem (x^2-x+1)/(x^2+x+1)=y

Its value is negative when 1/3<=y<=3. since a>0 its minimum value has to be (1/3 +3)/2 = 5/3. How is it 1/3 and how to find the maximum value

Re: Quadratic Equation
by Total Gadha - Tuesday, 8 July 2008, 03:56 PM

Hi Raj,

y is not a quadratic expression, it is a rational expression in quadratic. How are you applying the rule?

Total Gadha

Re: Quadratic Equation
by ankit sharma - Tuesday, 8 July 2008, 09:17 PM
  that is an amazing picture of some musician.i like
and no second thoughts about the article . it rocks as usual
Re: Quadratic Equation
by ATOM ANT - Wednesday, 9 July 2008, 07:20 AM
Clarify my doubts pls.
Re: Quadratic Equation
by Total Gadha - Wednesday, 9 July 2008, 09:14 AM
  Hi Atom,

1. x2 - 4x + 4 = 0, 6x - 9 - x2 = 0, etc.

2. x2 - x + 4 = 0.

3. Yes.

I think I have covered the change of sign thing in the chapter. Check. smile

As for your copycat- 1 doubts, send me a mail.

Total Gadha
Re: Quadratic Equation
by ATOM ANT - Thursday, 10 July 2008, 04:44 PM
  Thank u sir.. Will send my doubts tonight.
Re: Quadratic Equation
by naga kiran kosuru - Friday, 11 July 2008, 08:24 PM

Hi TG,

In the reply posted to ATOM, how x^2 - x + 4 touch x-axis only once?

i think it shd have two roots... pl comment....

And, how a quadratic eqn with imaginary roots is plotted on a graph..(if possible)....

Tnx in advance..

Re: Quadratic Equation
by abhi raj - Friday, 11 July 2008, 09:02 PM
  hi naga,
      x2-4x+4  touch x-axis only once as it has only one root i.e 2 or u can say that both the roots are same so it will touch the x-axis only once.
And as far as equation x2-x+4 is concerned  it  does not have any solution or it has imaginary roots which is ans to ur ques .
Re: Quadratic Equation
by Gul Gul - Friday, 11 July 2008, 09:15 PM
Re: Quadratic Equation
by Rahul Aggarwal - Thursday, 17 July 2008, 05:28 PM

Thanx sir for a beautiful article yet again...

Re: Quadratic Equation
by Hungry Gadha! - Monday, 21 July 2008, 02:23 PM

Hi TGsmile
How are you doing?

As usual TG rocks with his QA lessons, no question about it. So nothing to say about it.

Yeap…I’m very much elated to share the same kinda feeling whatever you have said on ‘entrepreneurship’. Running own firm and giving hope & life to few people…wow, what a feeling…just that’s gonna be one of the greatest moments of a life. Yeap…I love to  feel  that…that’s the sole reason  why I’m getting into MBA…otherwise no mean for me doing mba…smile yeap sir…in future, you will see me…your Hungry handling small business…for sure! After all that’s my ultimate goal of a life… Absolutely TG…of course, I’ll take loads of Gyan from you on that front too... smile

Great words inspires me…thanks a lot for them TG.

Take care


Re: Quadratic Equation
by anuj hembrom - Wednesday, 23 July 2008, 01:56 PM
  hi sir,
         thnx for the valuable article, as you have covered almost everything
         but an article on functions is desperately missing, as regard to its              importance in exams like CAT  & XAT hope you'll consider  it.
Re: Quadratic Equation
by Jegathiesh P - Thursday, 24 July 2008, 02:52 AM

Hi Sir,

  In the illustration of finding the maximun value of the expression 1+2x-3x^2, the maximun value of the expression f(x) is 4/3 and it occus at

x= -1/3 and x=1 and not at x=1/3 (what specified in the article). Correct me if I am wrong.





Re: Quadratic Equation
by Total Gadha - Friday, 25 July 2008, 07:35 PM

Hi Jegathiesh,


you are talking about the roots. I am talking about the maximum value.


Total Gadha

Re: Quadratic Equation
by Anamica Sinha - Sunday, 10 August 2008, 11:59 PM
  thanks.... this is really helpful... smile
Re: Quadratic Equation
by Shiladitya Mukherjee - Thursday, 30 July 2009, 10:28 AM

Hi TG Sir,

 I've a small doubt regarding the last problem -

For b2 - 4ac >= 0 we can already conclude that (y-1/3) ( y-3) <=0 , then why are we going for the next statement?




Re: Quadratic Equation
by aashish biala - Tuesday, 18 August 2009, 06:01 PM


thanks a ton for such a nice post. you are doing a great job. you cannot immagine how good i am feeling from within. Commendable is the word for your effort TG.


aashish biala

Re: Quadratic Equation
by aashish biala - Tuesday, 18 August 2009, 06:04 PM

hi Shiladitya,

here in this question y= x^2-x+1/x^2+x+1. So, the range of y is actually the range of that expression whose minimum and maximum value is being asked which is 1/3 and 3 respectively. Hope it is now clear.

aashish biala 


Re: Quadratic Equation
by Dev Raj - Thursday, 20 May 2010, 07:02 PM
  TG sir,
These are  probably the most written words around here but i shall still pen it down... smile
Your article instills much needed confidence in me....
Thank u sir....

Also sir,
agar kuch questions mil jaayein linear, quadratic and special equations par to maza hi aa jaye sir..........

Re: Quadratic Equation
by nick depp - Saturday, 5 November 2011, 03:47 PM
The perimeter of a rectangle is 80m and it,s area is 400m^2.Find its legnth & breadth ?

please provide me the solution of this quadratic Equation.

Re: Quadratic Equation
by suraj saxena - Saturday, 5 November 2011, 06:09 PM

X^2 -40X+400=0



Re: Quadratic Equation
by sharmil kothari - Sunday, 6 November 2011, 01:38 AM
  i think its an rectangle so both the sides are not equal
so ans is 16*25=400
Re: Quadratic Equation
by manik bhardwaj - Wednesday, 2 May 2012, 07:09 PM
  Hi All,
I have one more doubt in quadratic equation as:

Find the remainder when 3x^5+2x^4-3x^3-x^2+2x+2 is divided by x^2-1

As x^2-1 can be resolved into (x-1) and (x+1) and then we can input the value at f(x) for 1 and -1, but still im not able to get answer correctly.
request yours help
Re: Quadratic Equation
by TG Team - Thursday, 3 May 2012, 11:49 AM

Hi Manik smile

3x5 + 2x4 - 3x³ - x² + 2x + 2 ≡ 3x(x²)² + 2(x²)² - 3x(x²) - x² + 2x + 2 ≡ {3x(1)² + 2(1)² - 3x(1) - (1) + 2x + 2} mod(x² - 1) ≡ {3x + 2 - 3x - 1 + 2x + 2} mod(x² - 1) ≡ {2x + 3} mod(x² - 1).

Kamal Lohia 

Re: Quadratic Equation
by Dips Belldcat - Sunday, 29 July 2012, 08:00 PM
  Hi Kamal/TG,

Can you please help to understand & solve the following problem:

If both the roots of the quadratic equation: ax2+bx+c=0 lie in the interval (0,3), then where does 'a' lie?

I am not able to understand the problem completely;so your explanation on how to reach the solution will be helpful.

Re: Quadratic Equation
by saurav garg - Saturday, 13 October 2012, 01:37 AM
  dada.............u r awesome tausome!!!!!!!!1help 2012 cat aspirants tooooooo plzzzzzz!!!!!!!whatts the pattern this time if u have come know from somewhere plzzzzz tell and i have sme seriosu problems in this quad sad :/
Re: Quadratic Equation
by Ramesh Rawat - Wednesday, 10 July 2013, 02:07 AM
  Hi Sharmil,

16*25=400 correct..but that does not give the perimeter to 80 as 2(16+25)=82....
So the correct answer is a square of 20*