Total Gadha-Quadratic Equations

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Quadratic Equation

by Total Gadha - Saturday, 5 July 2008, 04:21 AM

I have not written for a while for my CAT 2010 students, not because I didn't want to but because the explosivegrowth of Totalgadha.com and TathaGat kept me busy in multidimensional roles. Gone are the long eveningwalks, leisurely problem-solving sessions and book readings. Now my time is spent in hurried classroomsessions, editing worksheets, answering incessant phone calls, and managing a rapidly-growing team. Thepleasures and pains of entrepreneurship are numerous. Not that I am complaining. It feels good to see that anidea which was once a passing thought has blossomed into something real. It is heartening to see that you cando a lot of good in this world. TG.com was once a thought. Now it is a reality. It would give rise to more realitiesTomorrow, there would be something better than TG.com. There would be better thoughts. And in the end, itwould be the students who would benefit the most by the new realities. It is reason enough to rejoice, pain ofentrepreneurship notwithstanding.

One more CAT is approaching fast. There is already a tightening in my stomach, a lump in my throat. If I couldhave my wish, I would want all my students and TGites to clear CAT. But this is not possible, and in the end, lifewouldnt be interesting without a good mix of victories and defeats. No matter what happens on the D-day, I

hope that the students dont stop learning at least. Amen! So here is it ladies and gentlemen, a fruit of painful labour.
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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 inthe CBT Club this week.

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Re: Quadratic Equationby 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 - 10

- 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.

Regards

Amit.

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Re: Quadratic Equationby y v - Saturday, 5 July 2008, 03:35 PM

TG sir...You ha ve forgotten to add -6..So the answer is -31 a s Amit has pointed out...Article was very use ful sir...Please post an a rticle on time and work

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Re: Quadratic Equationby ATOM ANT - Saturday, 5 July 2008, 03:51 PM

TG sir,

I have few doubts.

1.Can you give me a n exa mple of a pa rabola that touches only x-axis?

2.You have given three different curves for the quadratic equation with a>0 and a


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Clarify my doubts pls.

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Re: Quadratic Equationby Total Gadha - Wedne sday, 9 July 2008, 09:14 AM

Hi Atom,

1. x2 - 4x + 4 = 0, 6x - 9 - x 2 = 0, etc.

2. x2 - x + 4 = 0.

3. Yes.

I think I ha ve covered the change of sign thing in the chapter. Check.

As for your copycat- 1 doubts, se nd me a m ail.

Total Gadha

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Re: Quadratic Equation

by ATOM ANT - Thursday, 10 July 2008, 04:44 PM

Thank u sir.. Will send my doubts tonight.

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by naga kiran kosuru - Friday, 11 July 2008, 08:24 PM

Hi TG,

In the reply posted to ATOM, ho w x^2 - x + 4 touch x-ax is 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..

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Re: Quadratic Equationby abhi raj - Friday, 11 July 2008, 09:02 PM

hi naga,

x2-4x+4 touch x-ax is only once as it has o nly one root i.e 2 or u can sa y that both the roots are sa me so it will touch the x-axis only once

And as far as equation x 2-x+4 is concerned it doe s not have any solution or it has imagina ry roots which is ans to ur ques .

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Re: Quadratic Equationby Gul Gul - Friday, 11 July 2008, 09:15 PM

Lovely...!

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Re: Quadratic Equationby Rahul Aggarwal - Thursday, 17 July 2008, 05:28 PM

Thanx sir for a beautiful article yet again...

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

Hi TGHow are you doing?

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

Yeap Im very much elated to sha re the sam e k inda fee ling whatever you have sa id on entrepreneurship. Running own firm andgiving hope & life to few peoplewow, what a fee lingjust thats gonna be one o f the greatest mom ents of a life. YeapI love to feel

thatthats the sole reason why Im ge tting into MBAotherwise no m ean for me do ing mba yeap sirin future, you will seemeyour Hungry handling small businessfor sure! After all thats my ultimate goal of a life Absolutely TGof course, Ill take
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loads of Gyan from you on that front too...

Great words inspires methanks a lot for them TG.

Take care

Regards,HG

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Re: Quadratic Equationby anuj hembrom - Wedne sday, 23 July 2008, 01:56 PM

hi sir,thnx for the valuable article, as you have covered almost everythingbut an article on functions is despe rately missing, as regard to its importance in exa ms like CAT & XAT hope you'll consider it

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Re: Quadratic Equationby Jegathiesh P - Thursday, 24 July 2008, 02:52 AM

Hi Sir,

In the illustration of finding the maxim un value of the e xpression 1+2x-3x^2, the maxim un value of the ex pression f(x) is 4/3 and it occus

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

Regards,

Jegathiesh.P

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

Hi Jegathiesh,

you are talking about the roots. I am talking about the max imum value.

Total Gadha

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Re: Quadratic Equationby Anamica Sinha - Sunday, 10 August 2008, 11:59 PM

thanks.... this is really helpful...

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Re: Quadratic Equationby Shiladitya Mukherjee - Thursday, 30 July 2009, 10:28 AM

Hi TG Sir,

I've a sma ll doubt regarding the last problem -

For b2 - 4ac >= 0 we can already conclude that (y-1/3) ( y-3)


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thanks a ton for such a nice post. you are doing a great job. you cannot imma gine how good i am feeling from within. Com menda ble is theword for you r effort TG.

cheers!!!

aashish biala

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Re: Quadratic Equationby 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 a ctually the range of that expression whose minimum and m aximum value ibeing asked which is 1/3 and 3 respectively. Hope it is now clear.

aashish biala

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Re: Quadratic Equationby Dev Raj - Thursday, 20 May 2010, 07:02 PM

TG sir,

The se are probably the mo st written words around he re but i shall still pen it down...Your article instills much nee ded confidence in m e....Thank u sir....

Also sir,agar kuch ques tions mil jaayein linear, quadratic and spe cial equa tions par to ma za hi aa jaye sir..........

Regards,Dev

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Re: Quadratic Equationby nick dep p - 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.

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Re: Quadratic Equationby suraj saxe na - Saturday, 5 November 2011, 06:09 PM

VERY SIMLPE2(L+B)=80L+B=40L*B=400

X^2 -40X+400=0

(X-20)^2=0

L=B=20

HAVE FUN!

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Re: Quadratic Equationby sharmil kothari - Sunday, 6 Novem ber 2011, 01:38 AM

i think its an rectangle so both the sides are not equ also ans is 16*25=400

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Re: Quadratic Equationby manik bhardwaj - Wedne sday, 2 May 2012, 07:09 PM

Hi All,I have one more doub t 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 correctlyrequest yours help

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by TG Team - Thursday, 3 May 2012, 11:49 AM

Hi Manik

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

Kamal Lohia

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Re: Quadratic Equationby Dips Belldcat - Sunday, 29 July 2012, 08:00 PM

Hi Kamal/TG,

Can you please help to unde rstand & 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 unde rstand the problem completely;so your explana tion on how to reach the solution will be helpful.

Regards.

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Re: Quadratic Equationby 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 some where plzzzzz tell and i have sme seriosu problems in this quad :/

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