hello my dear are you all super duper excited students equations so are you all ready great in the I will do that gri shank nice to see you welcome ASP so I think you guys at stay safe and utilize this time to study rather utilize it to study [Music] okay confidence I want you to carry it until your board exam got it so let's get into it classmates juniors seniors cin reles I said I want to make them access very good quality education not only academics but also strategies iny I love problem solving 11 I used to solve so many questions I will quickly introduce myself and I did my engineering from I medras so IAS number one and the exams I was one of the state Toppers in background we can have a marathon session we can solve questions exed we need support and involvement from students we can reach Great Heights because there is so much I want to teach all of you and I want to give you a lot of confidence and I want you to reciprocate we will make it happen don't worry soang let's get started session G so in your road map qura Ro and product of roots in relationship with the coefficients of roots practice questions we reach success we have completed this chapter okay that is what I ask all of you open mind maybe you will be able to understand it you'll be able to follow and solve questions okay so let's get started my dear boys and girls equ pols polom you have to recollect so pols do you all remember questions so Pol it is any expression of the form a not + A1 x^ 1 + A2 X x 2 plus A3 x 3 and so on all the way up to a n xn so are you all clear is the highest power of a polom so example so P of xal to X plus x^ 4 + 3x² plus 100 x so in the poe can anybody tell me let's see who's telling it correctly San Levan you are amazing kav super kav Guru level Guru gam lak superb gatri fantastic you guys are super awesome Surya fantastic superb you guys are fabulous keep it up so so this is a fourth degree Poe polom of degree 2 quadratic it is a polom which has degree two so General quadratic equation a x² plus BX plus c equal Z you all like it equation equal to Z that is quadratic equation are you all clear how many of you are happy with it I hope all of you enjoyed it now let's move forward so the standard form of this equation quadratic equation standard form a x² plus BX plus C is equal to C constant term constant term A a is called as leading coefficient a is called as the leading coefficient B is the coefficient of x b is nothing but coefficient of x soang in the quadratic equation can you tell me what are a b and c so a b c can you all please tell me I want you to be attentive I want you to participate okay so starting example very Gooding terming it is you are wrong please correct it isus so B is minus 5 it is not plus five so constant term constant please don't forget that so everybody is learning everybody is growing no problem let's move forward shall we move so I have given you examples the it is looking like x² it is looking like X Cube so it is just cartoon representation so xare Square gra they have shown it through the hor got it so I hope you all enjoyed it now let's move forward so quadratic equation can you all please TR out okay I want all of you to take out your weapons weapon is youren okay kill this topic okay very good so everybody please try to do it pangla quick quick quick quick great so what is the answer so left hand side over X into X x² X into + 2 + 2 x - 1 into x - x -1 into +2 -2 X into x x into +21 into1 into +2 right hand side x into X x² up X into +1 + x up minus 3 into x - 3x - 3 into +1 -3 so X x square x² canc x- 2al you have- 2x minus 3 so you get you will get 3x equal minus1 line equation equation so a is wrong a equ very good so option b you guys are absolutely correct did you all love it so very good gatri Shankar fantastic Master art sadana Muresan very good Nal netra AAL super ajal Monisha fantastic PR Jes all of you are right great job so pasang yeah second one correct what is a plus b square a plus b square is a s square + b s+ 2 a a x b 2 so left hand side right hand side 4 into x 4x 4 into + 3 12 so + 4 + 4 - 4x + 12 left- 12 = you get x² minus 8al to M so quadratic equation so second one correct quadratic equation did you all enjoy so third and four and okay so let's see so you have X2 + 3x + 1 is equal to x - 2 s x² - 4 x + 4 so X have + B Cub is a cub + B Cub plus uh 3 a square B + 3 a b² so that is equal to what that is equal to 2x Cub minus 2x so simplif this will be a cubic equation so so you'll have a cubic equation in the last one did you all like it are you all happy yes I hope all of you enjoyed it pangla you guys are absolutely amazing keep it up very good very good way to heaven absolutely right good job you have to check it so if you want to watch it clearly settings higher video I hope all of you are clear so let's move forward then we shall proceed okay fantastic so yeah let's go faster okay so in the in the question try to form the quadratic equation so you have to be ready for it I have given you a situation okay so everybody please try to solve it two consecutive positive integers or product so I will take it as XG X+ so let X be a positive integer let let X be a positive integer so the two consecutive numbers are X and X+ one soct it is X into x +1 and the product 36 and the product 36C x² + x is equal 306 and you can write it in the standard form standard form if I was your teacher I will be happy so this is the standard form it will be better so you have to keep it in this stage are you all happy very good answer 17 and 18 did you all get it so answer x 17 X+ 18 okay so shall we move forward M did you all enjoy it okay so it's a nice question I hope you enjoyed it now let's move forward sir root n is Sir Sir root n is Sir root it is the value of x for which the equation is satisfied for example of the variable it is a quadratic equation I'm telling you put xal two is called as a root of the quadratic equation x² = 4 super did you all like it so satisfy xal 2 is a root of this quadratic equation superal so min-2 is also a root of this quadratic equation so I can say r is a root of this quadratic equation so what is your pet name everybody has a pet name at home so we have zero we have solution to check it okay so shall we go forward everybody great great so you see many pet names you have got in the chat great great okay let's go forward I hope you all enjoyed this so like I said root of the quadratic equation now it is the value of the variable for which for which the equation is satisfied okay the value of the variable X for which the equation is satisfied did you like this how many of you understood it can you all please let me know not I know I know why blood same blood anyway let's move forward I hope you liked it in the root I just showed you as an example okay so what is Root Root now it is basically the value of x for which the quadratic equation is satisfied the value of x for which the quadratic equation is satisfied value of root or you can call it Zer or you can call it solution I want everybody to try it along with me please do it I want everybody to solve I controlled it I learned from my students only obvious I learned from my students and jokes Club sir serious I'm not kidding I there is a club called as M jokes Club okay I I'll ask you one question what is the opposite of area don't tell okay it's a very tough question what is the opposite of area opposite perimeter answer area opposite okay I hope all of you I know some of you are Le laughing okay so so shall we get started okay so let's continue with with our discussion so half is a root of this equation so half root equ will be satisfied okay so equation satisfy so let's try to substitute it so X half squ plus K into half - 5x4 is equal to mutai okay so what do you have 1X 4 + K by 2 - 5 by 4 is equal to 0 so what is the answer so K by 2 - 5 + 1 - 5 + one - 4 by 4 is equal to0 K by 2 isal 1al option you guys are right m did you all enjoy it are you all happy with it pangla Frankie super very good you guys are awesome Jason let's go forward thank you I don't know who is Raju but anyway great so so methods of solving quadratic equations shall we all begin so Quadra equ already I hope you're all aware soling qu Quadra equation finding the value of x for which the equation is satisfied so for examp Quadra equation okay equ equ asking Ro solving a quadratic equation now it is basically finding the roots of the quadratic equation clear Super G G yes yes yes I got it okay I still don't know who that is even though I watch IPL okay so I'll check it out after the class okay so are you all happy very good very good middle term splitting splitting of middle term Quadra formul completing Square okay so are you all ready shall we go forward shall we move so in the so please go and solve NC okay delet okay okay I will give you very good meod so I don't want to stop you okay so P are you all super excited shall we get started kaves MV registrations okay exam useful I was very okay when I was school when I was in school I was quite naughty and I did I did well but 25 45 then I was able to get tamilnadu state rank five college and IND best college I Madras engineering and it was a great journey I enjoyed my college life it completely changed and I I absolutely loved it like I said the you have the registration link click on the link to register for m online it's up to you whatever you want you can do okay registration is completely free of cost I hope all of you will do it andang see the idea is not to become the topper I wanted to bring awareness I want everybody to utilize this opportunity especially those who are outside cities on the whole point I was a medalist from best college and the bestle I got the first rank so I got many good offers because what I'm saying is if you are somebody who's wanting to experience okay let's come back starting trouble sir starting trouble so I will teach you how to start start this don't worry are you all clear superus 16 plus 16us 12 12 step by step step I hope all of you are happy and with me don't get upset be be patient with me I want everybody I want all of us to grow together step second step on multiply a and C multiply a and C they take only C please remember it is C so I have to split into factors which will give me 16 and so 5 into + 12 so number add should give me 16 plus 16 sir easy sir plus plus correct plus into plus is plus so so okay are you allar you can write - 10 into - 6 you can write -2 into - 5 you can write + 12 into + 5 Poss Su should give you the middle term the sum should give you the middle term Sirus 10 into- 6 sum should give you middle term product should give you the midd term I'm going to split the middle term and so plus 16 I will write + 10 and plus 6 5+ 6 into x +al one of them is equal to zero and the other one is also equal to zero so xal -2 5x = - 6 x = - 6 by 5 did you all love it are you all happy okay so please try to write it once did you all enjoy it was it beautiful please everybody please not it down because I want to complete full portion in the whole chap I'm trying to give you one example will you all do that so that is the second advantage of writing your m shall we all go forward everybody please try to solve it come on guys I want you all to be fast I want you all to be fast quick quick quick quick t t great great online students online students to you will get five day space trip okay space camp trip space trip space camp trip ISRO space camp if you are a Topper in your particular class MV sat and with you I will arrange your travel I will bring you to Chennai and games that is my gift from vantu to all our Master students okay so utilize it Bon so b s Comm straight did you all like it are you all clear b² X and minus one I hope all of you are able to get that so x a a s x + 1 is 0 b² x - 1 = 0 x = -1 by a s root x = 1 by b s root Rend root super did you all like this are you all able to follow very good S V level s very good Jason superb you guys are absolutely awesome I want you to solve along with me that is when you learn best that that is when you will grow better so are you all clear PR so mam December 2 and 3rd December 9th and 10th Saturday Sunday December 2 and third is Saturday Sunday December 9th and 10th is also Saturday Sunday so you guys can write when whenever you want you can register it today okay very good so I hope you enjoyed it so completion of square method completion of square method so you can use quadratic formul you will be able to solve it it is not very difficult so don't worry don't don't feel bad you guys can do it soang completion of square deleted so I will say solve it by quadratic formula so solve it by quadratic formula if you want so the quadratic - 4 a so do you all agree do you all agree are you all happy with this everybody please make a note of it a one B minus 8 do you all agree with me on that so disc disc it is b² - 4 into a into C- 8 square- square plus 8 sare 64 - 4 into 18 72 minus 8 Which is less than zero discriminant less than Z you will have no real root if the discriminant is less than zero you will have no real Ro are you all clear everybody happy so shall I move forward is it easy Roots Ro okay so nature of roots you need to find out the discriminant discrimin discriminant B 4 a discriminant disc and distinct Roots distinct Roots discriminant greater than zero now you will have two real and distinct distinct Roots discriminant equal to zero now you will have two real and equal Roots but I'm just telling you so that you will repeatedly hear it from me discrimin when you are trying to find out number of did you all like it are you all happy very good I'm so glad you're all able to follow brilliant brilliant effort you guys are super duper awesome great so nature of roots how many roots are there what kind of roots are there real root only discriminant discrimin over so disc roots you will have dis Roots two and they are distinct equal two and two so equal Roots equal Roots two and two equ Ro two and three M example example examples so distinct roots and two real Roots discriminant positive positive now more than zero discriminant equal to zero now two real Roots which are equal discriminant less than zero in the case then you have no real Roots so + 18 is equal completion of square perf Square x² minus linear term 2 into are you guys able to understand that so x² and linear term Focus x square already perfect square minus in the 8 2x I'm trying to bring a minus B squ x² - 8X so it might be a part of a minus b square so a square 2 A+ b s so xus 2 x² minus 2 * of a into we have a sare - 2 a so a square - 2 a complete I need b square I need b square so b square now I need four square so I have to add and subtract Four Square so I have to add and subtract Four Square so I'll add four square I will subtract four square and already 18 so that is equal to zero cheria are you clear it nothing but x - 4² - 16 + 18 = 0 so I'll get x - 4 squ is equal to-2 so no roots how can a square of a number be negative that's not possible how can the square of a number be negative that is not possible it has no solution did you all like it please be very clear experience okay so I will I will try to help you out again so completing Square MEF sare Aus sare a square are you all cleara a squ + 2 A + B squ A + B square a minus b square a square minus 2 A + B squ form obvious minus so I will choose minus 2ab I will choose minus 2ab so minus 2ab - 8- 2- 8 and X are you able to understand are you able to follow so did you all like it so a² x² minus 2 a I have shown you clearly separately there now does it make sense I hope you guys are able to follow okay are you all clear so a s minus 2 I need to have plus b squ I need to have plus b Square Four Square will so I will add four square I will subtract Four Square also why because you cannot simply add four square you have to keep it consistent so I will add four square I'll subtract Four Square already blue circle A- 2 a + b square a square - 2 a + b square that is nothing but a minus b square that is nothing but a minus B squ so a b square- 16 + 18 - 4 S + 18 so - 16 + 18 - 16 + 18 is +2 so in the plus two right side in the plus two equality right side-2 so how can the square of a real number be negative that's not possible the square of a real number cannot be negative therefore it has no solution exam two years three years back 2019 are you all clear I will start if you want okay okay so NC nth and 10th sir so I have written I have done the solution of biology maths so biology Sandra and Maths for nth and 10th I would have done so please utilize it PA super did you all know that different quadratic please let me know three chapters only done okay so I will try to continue that and finish it I want you to regularly follow that channel and one more thing you will find it very very useful okay purposely I did it very slow I made it very slow so that everybody even if you don't know anything even if you don't know anything promise I'm telling you for sure you even if you don't know anything you'll still follow and okay please follow it record okay great so fast okay so next one is quadratic formula quadratic formula what is the quadratic formula so the roots of quadratic equation so a x² + BX + c equal Z okay a x² B cus plus or minus root of b² - 4 a c by 2 a equ we have two roots root of B 4 a c by 2 Aus minus B minus of root of B S - 4 a c by 2 a so quadratic formula which gives you the two Roots s very good super and I know NC Chan like I said I'm solving did you see that single question I'm giving you detailed explanation I'm giving you explanation so please go and check it out it'll be helpful soang I hope all of you are clear with the quadratic formula we will try to apply it and we will we will try some questions okay so 10 minutes please try to use it don't don't split the middle term use quadratic formula quadratic formula everybody please try to do it I want you all to be fast easy chapters you can easily get more than 70 80% I'm I'm not kidding arish it is possible and in 12th marathons December chemistry phys those sessions will be enough for you to score well inard exam okay so December Marathon both for 10th standard and for 12th standard please continue to support us okay so I want you to regularly follow the channel and utilize whatever we provide that is the best return you can give so biology teacher yesterday I introduced M to all of you 12 standard is such an expert biology so please follow that regularly great so qura b b c c 12 correct a plus one B+ 7 C+ 12 so quadratic formul quadratic formula is xal minus B plus or minus root of b² minus 4 a c by 2 a level so x = - 7 plus orus root of 49 - 48 divided 2 so X is equal to - 7 plus or minus < TK 1 so root 1 one so it will be - 7 + 1 by 2 - 7 -1 by 2 so the answer is-3 and-4 corre did you all like it was it good good Super so- 7 + 1 by two minus - 7 -1 by 2-3 and-4 did you all love it are you all happy with this my dear boys and girls superb you are all absolutely awesome so Pang some of the roots word problems will you all be there every day I want your participation tbook you will become much better ma will become better your level will improve you will see that so ready now we can work together and we can reach the sky okay so please do Sol you have a golden opportunity golden opportunity so the video you have your mvat exam so MV Mega vant scholarship test so free of cost all know where you stand to change to change your direction so one allia exam only changed my life full por you will be able to rock this exam so the P Bangalore Delhi online so you will know where you stand so please go try it chn offline yes chenn offline Exam Center it'll be a good chance to go see other people other students giving this exam and price level price 5 days space camp anal space camp ISRO is scientist five days space camp you will get drones you will get Mobile smart watches to be one number channel top rank Tam top rank you will get to spend one day with me and my team yes you will spend one day from breakfast to dinner I will arrange travel for you through and you guys can all come to Chennai and we'll spend one day fully to to to try to push you to realize how big this this is okay okay so some people will utilize this and you will come flying you will you will completely turn things around that is my satisfaction okay so all the very Math and Science 10th standard we have mental ability your aptitude maths and science main maths and science M for five Mar mental ability your thinking skills okay we have studied so much full portion science and math almost I wish you all the best don't forget okay and also if you can see here ninth standard 10th standard I keep solving 10th standard purple so Quadra equations I have Sol check it out okay okay that's about continue and I want all of you to come prepared continue Roots relationship with coefficients sum of roots and product of roots problem okay so word problems important board exam point of view stud okay great Ganesha I will upload again Ganesha I'll continue I will finish it off by DEC so that full ANC covered it'll be a great great asset for you guys I hope you realize it I will deliver okay great take care guys bye-bye