 speak up. Okay, so let's start and all the best to everyone. So here is the first question on the board. This must be easier to handle. You have seen this question already in all these questions are related to with subjects physics. So the first first equation first equation u square plus 2 s what is u in that u is initial velocity what is a in that acceleration what is s and so what is the assumption in this equation acceleration is constant acceleration is constant so this particular equation holds true for which kind of motion linear motion is linear motion very good second equation is v is equal to u plus at right and what is the third equation can anyone tell me sir sir s is equal to u t plus half at square no third c in this question the first one is equal to 2 s is that speed of the pendulum no you know this equation was found out by whom any idea no sir pi root over l by g was given by a very famous person who invented the telescope was a guy no who did i Galileo Galilei so he was uh in in the church and uh in the mass when he saw the chandelier move to and fro and that's where he performed this experiment okay very good so lots of people know and why is the reason what is the reason for this not being a polynomial pi exponent of the variable is not a whole number yes very good it's not because of pi those who are saying pi that's not correct it's because of the root right yes not because of the pi okay pi is very much allowed in any polynomial okay very good so first leader board i don't need to explain this i guess do i so this was just a warming warming up question very good oh my god seeram has just seeram within five milliseconds he has answered it seeram goes with nishant and then king tony north hsr national open school hsr he goes to okay anyways so let's go to the next question which of the following statement so there must be some easy questions also no so that you get trapped isn't it sir teaches how you trap you get trapped 20 times and you start you start trapping others okay because then we can learn the art and then we can make sure to avoid the trap the best way of learning is to make the mistakes commit the mistakes yourself you can't learn cycling by looking at someone else cycling you have to cycle yourself and fall down isn't it such a easy question sees that response is something which is disturbing isn't it so right so both the statements were actually true and the question was not true which of the following statement is not true okay and both the statements happen to be true okay so none of them are not true statement right so the degree of fx is zero is not defined you know that y is zero degree of z fx equals to zero not defined because fx equals to zero can be zero times x to the power of one million also and zero times x to the power of one trillion also which one should we take a billion also sorry so there is no defined right so this is correct statement all polynomials are actually algebraic expressions so this is also correct statement so both are true so where's the question of not being true none of them right so yes your accuracy now let me see accuracy one by two two by two two by two two out of two one by two see in the some people were so thrilled about being easy no you know easy means at times deadly see only 14 people got the correct answer it's such a small easy yes so that's the parallel issue no one is reading the question properly okay next here is the next question guys yes easy easy test is more tough try to do value of the polynomial okay so lots of x I can see in the list in the chat but still most majority of you got it it was simple one so f of minus one will be simply four times minus one to the power four wherever there is x you have to simply replace it by the value minus three minus one plus a minus one whole squared minus b minus one minus six and this is zero it's given right so if you check this is four plus three plus a plus b minus six is zero so a plus b was minus one right so if you square you'll get one so that means a plus b is equal to one upon a plus b is or no was it so difficult was it so difficult was it so difficult right so first one right we didn't need any extraordinary knowledge only looking at the question would have helped you never mind so I misclicked the correct answer that's more dangerous unforced error is like more dangerous don't do that okay so very good King Tony is on and one very good all of you keep it up next question you must know different types of polynomial so fx is a quintic polynomial and gx is a quadratic polynomial if degree of rx is one then degree of qx is basics of polynomial multiplication so what is quintic five wait quintic is five oh four is by quadratic or quartic so what is six so very good so it was five so if you know oh sad answer is three so fx is five degree five so x to the power five is your gx is quadratic so it's square so x to the power n plus this is something x power one like that isn't it so hence for LHS to match up with RHS you must have a degree five term which will come from only this so hence n has to be three yep so you are yes anyone four on four four on four these questions when it comes to you know NTSC's and all that it will take take five seconds to solve not beyond that so you have to have to improve to that level okay sad that today there will not be any hundred percent correct anyone okay never mind here is the three on three that's still better push me hundred percent Shivam Srivastava you did not get it correct Joni is ruling the show be careful with your calculations you have to only find number of zeros you know what a zero is zero of a polynomial is that value which reduces the polynomial to zero that where if that value of the variable which reduces the value of the polynomial to zero is called zero polynomial is called zero of the polynomial so need not be actually easy go by go by appearance it's neither tough if you know what a zero of a polynomial is you'll be able to solve it clicking is blender don't pay that phone on phone later let me see that is what I was expecting that's nice degree is equal to number of zeros yes correct degree is equal to number of zero very good so if you see this is a linear polynomial no it is not three because the power three terms are getting cancelled so you have to actually multiply this so if you see this is two x cubed then minus three x square just because there is a degree three term need not mean that it is a degree three polynomial you have to simplify this so two x cube minus three x square plus four x and I told you how to simplify keep the same degree a same order sorry same power terms together and quickly write like this and then here you'll get two x square and then you'll get minus two x cube and then you will get minus x and then you'll get plus x square so I like plus x square and then yeah that's it and plus two x square so if you see this goes so yes sir could we have replaced the values as well which values so like x equals to a value and then try no never so why because you have two values not helping you you have to find out how much is the highest power of x in this case if you see this all goes these all gets cancelled so only linear terms are left so hence one it's a linear if you simplify this you'll get linear polynomial so you I knew that people will just see x cube and they will mark it as three and hence get it wrong okay right so are you see I do not have the intention of making you or you know what do you say I don't want to feel or make you feel bad but you also need to learn where you are going to you know get stuck and get confused and mark wrong answers so that's the learning and the result shows it that you are too tempted to mark the answer see the top five and one more only four out of top ten got the right answer okay only yep good next next question this you should be able to solve easy one but be careful with the signs these options are closer you know how to find a zero we discussed in the class also right last 20 second guys very easy question I believe why what happened Aditya three two one oh my god lots of people are lots of people are making a mistake here why x how many x x x x it was very simple you have to simply factorize it and equate to zero what is a zero of a polynomial that value of x which makes the polynomial itself zero so this is zero okay so if you see you can factorize it like this three root three minus two root three x 18 so mix of previous grade or not previous grade previous chapter this thing is well is it so hence you can take x common and you'll get x minus three root three and you'll take minus two root three common and you'll get x minus three root three right is equal to zero so if you factorize it you'll get x minus three root three and x minus two root three this is the factorization and this is equal to zero you have to find those values of x which reduces this to zero what are the possible values of x which reduces it to zero so you have equate each one of them separately and you would have got that so x is either three root three or x is two root three so this question required knowledge of knowledge of factorization have you not done this kind of factorization yes no no unnecessary talk class class affair in the class in school leave everything in school talk about problems here screen share is bleaching a bit why is it is it fluctuating or something flickering so it's actually slow what is slow the screen share like it takes like some two minutes next life no it isn't is it for me maybe because of the internet or something like that sir it's fine for me it's lagging a lot screen is lagging yes sir it's lagging a lot it's fine we see the results a lot later again oh is it so shall I reshare wait so I think it's my it's my problem so it's my internet okay let me let me stop sharing and share again okay let me see started sharing once again enough is that fine now we'll see anyways next leaderboard three one two three four in top good nice kanya is this tanya c inr is it tc tc oh tc good transfer certificates very good tanya right and then pratham big foot naffle oh you have so so big foot a square inr who is this gentleman sir it's me me means the aditya oh aditya oh and who aditya i pr y pr namradan abhuni bharat and anish anish is which which is cool anish naffle okay good nice next question yes is that 2019 it will stay for another six months i like i love every year very much so next year you will see 2021 lot many times especially these pr m o r m o they will give you something related to 2020 so what is the or 2021 so what does this mean what is the message that the number actually doesn't have much of a significance now that i have told you the catch omitted remember it one thing is for sure you will give examples of this year to your next generation shallow very good so cool okay okay okay okay still not many people are getting correct answer remainder theorem direct application no nothing needed remainder theorem was needed in this so the remainder theorem so fx is equal to x to the power 2020 minus 4 x 2019 right so remainder is simply nothing but f minus 1 f minus 1 is the remainder is it so hence it is minus 1 to the power 2020 minus 4 times minus 1 to the power 2019 now don't tell me that it is difficult to calculate the power of this thing so this is 1 minus and plus 4 because minus 1 to the power 2019 is odd so it will be minus 1 so minus 1 times minus 4 is plus 4 is 1 plus 4 okay yes let me see your accuracy rates now write your accuracies all of you 6 by 7 very good 4 by 7 5 by 7 1 by 2 4 by 7 1 by 2 5 by 7 6 by 6 who's 6 by 6 9 by 6 path jen you are from some other world of 9 by 6 sorry who got 6 by 6 17 by 17 this is like be serious guys no such spamming okay very good show up next question none of none of you are on 100 percent 7 attempted and 7 correct so we need to reflect on this hmm okay vihang pratham king tony came third tanya roshan shivam a square ruthvik and kavary kavary is a new entry very good next question if f 0 f 1 and f 2 are all 0 then the polynomial f x can be so i hope you would have done this correctly okay 18 people have said x square minus 3 express sir yes sir i was not able to choose the option at all it's still stuck in the option screen and it's shown i have time and it's stuck in the same screen barrage is it yes sir sorry barrage you can't really help in that you know you have to just reload at times it gets stuck here no problem you you mark it correct did you get it right i wanted to ask you so f 0 is so you know so you know the moment 0 0 is 0 by factor theorem x minus 0 will be a factor of polynomial effects whatever this effects is x minus 0 similarly x minus 1 will also be a factor and x minus 2 will also be a factor right so hence this would be the polynomial is it right so this was the answer raga what was that symbol what is that did you understand this how did i get this guys clear or not is that clear hello yeah anything anything no it can't be b because there are three zeros that means there are the degree has to be three so yeah so we have true false today yes so for me this question and the last both the question just says my answer is wrong when i click the same the correct answer did you did you get the right answer yes sir i clicked on the right no problem just mark that accuracy which i am monitoring i'm just monitoring your accuracy nothing else could you please explain once again once again so if we have a you know by factor theorem what is factor theorem factor theorem says that if you have a polynomial fx if you have a polynomial fx okay then x minus a will be a factor right x minus a will be a factor of fx if f of a is 0 right this is what we learned isn't it now if f of 0 is equal to 0 that means x minus 0 was a factor of that fx similarly if f of 1 was also 0 that means x minus 1 was also a factor of fx and since f2 is also 0 then x minus 2 was a factor or is a factor of fx that means there are three factors for sure okay so fx is x minus 0 times x minus 1 times x minus 2 this was fx okay so hence if you multiply this this is nothing but x times x square minus 3x plus 2 hence x cube minus 3x square plus 2x now did you understand yes the person who asked the question okay so let's see who is yes sir um if you calculate the c doesn't it work as well yes it does work for i was that but who's this yes it does work for c as well so did you mark c i mark c no mine so you can count that as in c as well okay chalo so vihan is now on top so i was just waiting if someone picks up a hat or not it's only pratham could pick good nice okay so let's go to the next one but since pratham there was only three factors so hence you can't have but yes equal factors can be counted no worries do this very simple so all the questions will be linked to previous chapters as well tanya what is meant by division division division division division remainder theorem factor theorem whatever theorem all are linked together factor theorem remainder theorem are same okay very good so most of you could do it it was very simple question i don't know you had to just simply you know factorize this part fx was plus simply 1 minus x 1 plus x and 1 plus x to the power 4 okay so if you divide this thing by 1 plus x or x plus 1 what will be the remainder what will be the remainder if you divide this this gets cancelled right so hence remainder is okay got it anyone wants more explanation to this this was see 10 seconds not even 10 seconds yep right so this one very good let's see the result still people are making mistakes taking time 9 70 who was the fastest hurry tau was fastest great good she took 9 something 70 seconds milliseconds shallow next question guys on screen if tx q plus p qx square minus 36 x plus 20 leaves the remainder 0 and divide by x minus 1 and 2 to the power q is equal to 128 to the power p then guys no cross talk no cross talk please groove refrain solve questions everything related to the question on the board let's discuss this out and the varieties of it paying attention and getting good score in camon all are linked if your accuracy is not 100 you should be disturbed but why is it that so and we need to work for that so try to improve that one instead of talking about tangential stuff pranav is always around some gang what is this gang stuff gang is a negative word use some good word team maybe disturb the gang so pranav gangster disturb boys boys okay so but you only told you a part of a math gang no i would i told you i was a part of a group which was named bajrang dull it was dull not great but a good something wrong in question let's see 23 people have got it correct that's nice very good okay yes again no spamming then guys doesn't look good no no don't copy paste stuff on chat i'm i'm continuously looking for who was who's sick who's saying x tanya says x anyone else okay so they go x minus one that means what does factor here i'm sorry yeah so when divided by x minus one what does it mean it means that f of one will be zero by factor zero because it leaves the remainder zero when divided by x minus one so f of one must be zero what is f one f one is p plus q minus 36 plus 20 and this is zero that means p plus q is equal to 16 isn't it p plus q 16 also two to the power q so exponent revision revision of exponent two to the power q is 128 p 128 p means two to the power 7 p right isn't it so hence q is equal to 7 p q is equal to 7 p now if q is equal to 7 p you can deploy it in this equation and write p plus 7 p is equal to 16 so 8 p is equal to 16 that means p is equal to 2 the moment i'm sorry how did you get 7 p 2 to the power q is equal to 2 to the power 7 p when will that be possible so the base is same exponent has to be same in an equation so 2 to the power 2 to the power x is equal to 2 to the power 2 that means x is equal to 2 isn't it here same ways q is equal to 7 p because the base is same so q is equal to 7 p so the moment i get q is equal to 7 p i put p plus 7 p 16 so i got p is equal to 2 if p is 2 q has to be 14 why because sum of p and q was 16 so 2 into 14 was what we needed to find out p q 28 below anyone wants more explanation anyone wants menti code is here 96724 so this time the which shows the time didn't even appear on my screen what didn't appear time yes that bar thing that shows the time oh it didn't come in your screen you're on a pc yes sir oh i don't know you're on um what what is that chrome right yes sir it's not because i am also using the same thing i'm using chrome and i'm you know whatever is there the same thing i'm also using maybe some maybe some no i you know your answer and your solution right kahoot is to to you know to put in equations over there becomes very difficult okay next yeah quiz is the same very very elementary okay so what is a factor you again use factor theorem a factor if if x minus one is a factor then f of one is zero that's the knowledge use the same thing if x plus a is a factor of fx and gx as well so hence and we get two relationship and then solve for it these are so close but it's not that hard you don't need to know option was very straightforward very very clear oh my god oh my god that means see if i solve it you will say how easy x plus a now all of you i must ask you okay now no chat there no chat you are if you are missing out only nine people getting it correct is a point of concern all of you now pay attention to the screen and tell me if any of the step is not understood by you now x plus a is a common factor stop chatting all of you i'll ask and then start hold hold hold hold hold hold now x plus a is a common factor that means f of minus a will be zero do you agree say why do you agree say why f of a will f of minus a will be zero similarly x plus a is a factor of gx so do do you agree for this as well gf minus a says how okay x plus a is a factor prove factor theorem what is factor theorem factor theorem if x minus a is a factor of fx then f a is zero yes or no right so if instead of x plus a i would write so instead of x minus a x plus a is a factor then f of minus a will be zero is that understood prove clear or in doubt right so f minus a is zero g of minus a is zero so if i put f of minus a you will get what a square plus pa plus q is zero and similarly a square plus la plus m is zero yes or no both are zero that means a square plus pa plus q is equal to a square plus la plus m both are zero this goes a square and a square goes if you take a common you'll get p minus l and you'll get m minus q what was confusing so a is m minus q upon p minus l right not possible right then p minus l is in the denominator so not possible right only this p minus q cannot be together p and l were together so not possible i'm sorry yes no problem so take minus time common so can i can i not write this as now this is this much is it trapped no same thing right if you take minus common from both top and bottom so i have written five upon seven isn't five upon seven equal to minus five upon minus seven both are same right so hence if you see this is nothing but same as m minus q by l minus p now become very very comfortable and familiar with all these tricks how to take minus sign and all that okay clear let's see but only nine people got it correct so that's not very see a lot of people have got it wrong okay only one person pratham very good pratham nice good and he is on first position next question so when are the true and false questions starting in 2020 who's this who's who asked me this question arith kya ask true and false questions are starting on june 23rd 2020 at 8 52 and 36 okay last five four three two one very very easy question okay okay okay okay okay okay okay uh good maximum number of people are correct that's good okay what happened so this was not to be confused this was nothing but if you take actually power five as y simply so what will happen this entire thing becomes y to the power 10 plus one is divided by y plus one right y to the power 10 plus one is divided by y plus one so it will be let's say this is f y so by remainder theorem remainder will be simply f of minus one right what is f of minus one so put minus one wherever y is there so minus one minus power 10 plus one which is equal to two so two is the f y yeah f of y so you have assumed x to the power five to be y right didn't understand once again the culture no problem please understand these the these type of problems will be very very so x to the power 50 plus one effects on say it effects yeah then next is uh you are dividing this by x to the power five plus one right you're dividing this by x to the power five plus one what does it mean so if you consider x to the power five to be y okay so what will this function become is equal to y to the power 10 plus one isn't y because x to the power five to the power 10 plus one is y to the power 10 plus one so function in y is this right now if you're dividing this by y plus one divide this by y plus one what will be the remainder by remainder theorem it will be simply f of minus one so hence it is minus one to the power 10 plus one minus one to the power 10 is one plus one is two so this is a remainder did you get it now all of you are it yes or no confirm yes yes okay great now get ready for the for the what true and false eight seconds to answer five questions okay okay two and false five questions eight seconds to answer and anything from previous chapters will also be there okay here you go already within two three minutes it will be over so all of you are ready yes confirm right confirm confirm why come on come on come on okay yes we start it here first question very fast okay let me see oh my god what some of two irrational number is always irrational number no not necessary sum of two irrational numbers need not be right root two minus root two is yes correct so hence all all people please correct your knowledge so you asked for some right sum of two yes correct the other person the other person do it root two minus root two okay some difference is a form of sum is that okay yeah right very good next subtraction is a kind of addition only adding negative negative thing to something okay anyways so this is your first number of roots of a given polynomial is equal to the degree of effects this should be most of you have got it correct yes it is indeed number of any types of root it can be complex root also no problem but then number of roots will be equal to degree of polynomial remember this next leader board so lots of shuffle shuffling happens in the last five questions okay let's see okay next question it gives you some extra time to read the question also okay this should be very very easy oh my god oh no why so i clicked false words here i'm wrong just a minute yeah so the question was this is the polynomial of degree one it's false right so what is the answer false only it's not a polynomial do you get that is it a polynomial that's the glitch maybe but then it's a false statement right there's no it's not a polynomial only okay next why did you why do you think it's a degree six at max what was the degree eight right that looks like that sir it's two come on it doesn't look like that by by any chance is it x square times two to the power four so even i thought it was a z i have a question and even come for me it's a two like that even i thought it was z that looks like it clearly looks like two it looks like z is this but we were trying to answer really fast and we tried to the question and even come for me so it looks like that anyways so this is the answer this was two to the power four times x square only the order was changed so degree was five okay never mind shuffling shuffling shuffling last question of the evening guys ready and it's here and the answer was oh again right why all zeros of this are not integers yes they are not integers because one is half if you see one zero is x equals to one and another zero was two x minus one is equal to zero so x is equal to half okay so all zeros are not integers true okay did you understand did you understand all of you got it any clarification needed for this so now you know after this session how to find out zeros equate the equation or the polynomial to zero factorize it try to find out zeros okay then we learned about factor theorem remainder theorem where to apply the questions will not be that straight forward and and what else learning is again in this question which all question was this is why to the power minus one this is not a polynomial right then this is a fact we already know this one some of two irrational numbers maybe zero okay when x to the power 50 plus one is divided by this so this is where this power was troubling you so now you know how to solve such kind of problems and yep all yeah any question any problem any of the problem any of these questions okay so final leaderboard of the evening very good so vhans maintains the lead very good and congratulations to you then squire in our niche then shri jengosh mr shiva sirvastava bigfoot who has krishna vignesh kavari and harita congratulations guys well done keep it up and yes but before you leave your accuracy please accuracy this is all okay accuracy accuracy accuracy please 11 by 17 okay how many questions did you get right today 13 by 16 okay good 12 by 17 12 by 17 12 by 17 15 by 17 very good aditya 15 by 17 14 by 17 14 by 17 15 okay 12 by 17 11 by 17 14 by 17 14 11 no problem no problem very good so when trying to maintain that beyond 90% guys so 17 means as you know you must get more than 15 correct all of you all of you should get more than 15 correct then only okay fair enough so see you again tomorrow in the class bye bye take care and tomorrow is assignment time is thank you sir amazing good thank you if you have not done thank you sir please thank you sir bye bye so what was that thank you sir that's mentioned in the group please check thank you sir thank you sir thank you sir thank you sir thank you sir thank you sir