Total Gadha-Quadratic Equations

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Quadratic Equation

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

I have not written written for a while for my CAT 2010 students, not because I didn't want to but because the explosive growth of Totalgadha.com Totalgadha.com and TathaGat kept me busy in multidimensional roles. Gone a re the long eve ning walks, leisurely problem-solving sessions and book r eadings. Now my time is spent in hurried hurried classroom sessions, editing worksheets, answering incess ant phone calls, and managing a rapidly-growing team. team. The pleasures and pains of entrepreneurship are numer ous. Not that that I am complaining. It feels good to see that an idea which was once a passing thought thought has blossomed into something real. It is heartening to see that you can do a lot of good in this world. TG.com was once a thought. Now it is a re ality. It would give give rise to more re alities. alities. Tomorrow, there would be something better than TG.com. There would be better thoughts. thoughts. And in the end, it would be the students 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 There is alre ady a tightening 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 C AT. But this is not possible, and in the end, life wouldnâ€™t be interesting interesting without a good mix of victories and defeats. No matter matter what happens on the D-day, I hope that the students students donâ€™t 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 in the CBT Club this week.

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Theory of Equations Linear Equations Reply

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 - 6 =0 should be having minimum value as -31 (and not -25).

x2 - 10x

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.

Show parent | Reply


by 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 Show parent | Reply


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MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions Re: Quadratic Equation

by 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<0... what is the form of equation where the curve do not touch x -axis... is it like y = x 2 + k.. 3.Are parabolas neccessarily symmetrical ? and I would like to a dd a po int to your lesson. For any quadratic equation of the form a x 2 + bx + c = 0 for every single change of sign there is a positive root. eg: x 2 + 5x + 6 = 0 roots = -2,-3 x 2 -5x - 6 = 0 roots = -1,6 x 2 -5x + 6 = 0 roo ts = 2,3 Thanks a lot for the lesson.. Btw where shou ld I po st my do ubts on que stions from Co pycat-1... Unfortunately my previous po st was de leted. Show parent | Reply


by tinu doshi - Saturday, 5 July 2008, 08:56 PM hello sir, ex cellence is the word fo r u!!!!!!!!!!! Show parent | Reply


by amit kumar - Sunday, 6 July 2008, 07:12 PM hi tg sir, very nice article.ke ep p osting these a s they are really usefull Show parent | Reply


by Rajakannan R - Tuesda y, 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 Show parent | Reply


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 Show parent | Reply


by ankit sharma - Tuesday, 8 July 2008, 09:17 PM that is an am azing picture of som e m usician.i like it. and no second thoughts about the article . it rocks a s usual Show parent | Reply


by ATOM ANT - Wedne sday, 9 July 2008, 07:20 AM Sir,


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MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions Clarify my doubts pls. Show parent | Reply


by Total Gadha - Wedne sday, 9 July 2008, 09:14 AM Hi Atom, 1. x 2 - 4x + 4 = 0, 6x - 9 - x 2 = 0, etc. 2. x 2 - 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 Show parent | Reply


by ATOM ANT - Thursday, 10 July 2008, 04:44 PM Thank u sir.. Will send my doubts tonight. Show parent | Reply


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.. Show parent | Reply


by abhi raj - Friday, 11 July 2008, 09:02 PM hi naga, x 2-4x+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 que s . Show parent | Reply


by Gul Gul - Friday, 11 July 2008, 09:15 PM Lovely...! Show parent | Reply


by Rahul Aggarwal - Thursday, 17 July 2008, 05:28 PM Thanx sir for a beautiful article yet again... Show parent | Reply


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

Hi TG How are you doing? As usual TG rocks with his QA lessons, no question about it. So nothing to say about it. Yeapâ €¦Iâ€™m very much elated to sha re the sam e k inda fee ling whatever you have sa id on â €˜entrepreneurshipâ€™. Running own firm and giving hope & life to few peopleâ€¦wow, what a fee lingâ€¦just thatâ€™s gonna be one o f the greatest mom ents of a life. Yeapâ€¦I love to feel thatâ€¦thatâ€™s the sole reason why Iâ€™m ge tting into MBAâ€¦otherwise no m ean for me do ing mbaâ€¦ yeap sirâ€¦in future, you will see meâ€¦your Hungry handling small businessâ€¦for sure! After all thatâ€™s my ultimate goal of a lifeâ€¦ Absolutely TGâ€¦of course, Iâ€™ll take


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MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions loads of Gyan from you on that front too... Great words inspires meâ€¦thanks a lot for them TG. Take care Regards, HG Show parent | Reply


by anuj hembrom - Wedne sday, 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 despe rately missing, as regard to its

importance in exa ms like CAT & XAT hope you'll consider it.

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by 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 at 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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by 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 Show parent | Reply


by Anamica Sinha - Sunday, 10 August 2008, 11:59 PM thanks.... this is really helpful... Show parent | Reply


by 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) <=0 , then why are we going for the next statement?

regards, Shiladitya Show parent | Reply


by aashish biala - Tuesday, 18 August 2009, 06:01 PM hi,


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MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions 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 the word for you r effort TG. cheers!!! aashish biala Show parent | Reply


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 a ctually the range of that expression whose minimum and m aximum value is being asked which is 1/3 and 3 respectively. Hope it is now clear. aashish biala

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by 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, De v Show parent | Reply


by nick dep p - Saturday, 5 November 2011, 03:47 PM

The perimeter of a recta ngle is 80m and it,s area is 400m^2.Find its legnth & breadth ? please provide me the s olution of this quadratic Equation.

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by suraj saxe na - Saturday, 5 November 2011, 06:09 PM VERY SIMLPE 2(L+B)=80 L+B=40 L*B=400 X^2 -40X+400=0 (X-20)^2=0 L=B=20 HAVE FUN! Show parent | Reply


by sharmil kothari - Sunday, 6 Novem ber 2011, 01:38 AM i think its an rectangle so both the sides are not equ al so ans is 16*25=400 Show parent | Reply


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MBA|CAT|CAT 2011|CAT 2012|CAT Online|MBA 2012|MBA Entrance Exams|CAT Test|Preparation|CAT Questions Re: Quadratic Equation

by 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 correctly. request yours help Show parent | Reply


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

Hi Manik 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 Show parent | Reply


by 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. Show parent | Reply


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 some where plzzzzz tell and i have sme seriosu problems in this quad

:/ Show parent | Reply

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