Rank Booster Series- Quadratic Equation🔥 | CEE 2026 | PYQ'S +Important Questions | Prime Maths Assam

Added: 2026-05-24

[00:00:03]Send those students.

[00:00:13]Yeah, but the 20 questions.

[00:00:21]I do.

[00:00:35]Okay.

[00:00:39]I don't More than 12 hours. Like you say.

[00:00:56]Okay.

[00:01:03]Okay.

[00:01:10]Okay.

[00:01:20]Okay.

[00:01:29]So. I mean quantity.

[00:01:31]The ax squared. Plus bx. Plus c. 20.

[00:01:40]Alpha plus beta is equal to. Minus of. B by a.

[00:01:44]Your product of the roots will give you the call. Alpha into beta. Is equal to c by a. Alpha.

[00:01:52]Alpha and beta are key way.

[00:01:54]Roots.

[00:01:56]Okay.

[00:01:58]Alpha into beta. Money. money product of the roots sum of the roots, okay?

[00:02:06]Okay. So, discriminant discriminant b squared minus 4ac discriminant number condition discriminant equal to zero the equal roots that they Okay. equal roots discriminant greater than equal to zero real roots that they real roots 1 2 3 4 -1 -2 -3 and real roots going if they are three real roots money D is equal D less than zero imaginary imaginary roots Okay.

[00:03:03]imaginary roots money D less than zero imaginary X factorize if you B of minus B plus minus under root of B squared minus 4ac by twice A So, any theory money questions going on here Okay. So, it will be the question is that alpha and beta of the equation are the roots of the equation are the roots of the equation x squared plus px plus q is equal to zero. And I want to find out what was the alpha squared plus beta alpha squared beta squared First of all the alpha alpha plus beta is equal to minus B by A minus B Yeah, the minus by A X squared coefficient is 1 So 1 able alpha into beta money key C by A C money key Q we have to Q by 1 Okay.

[00:04:09]So eight number condition to I am beta alpha squared plus beta squared I mean alpha squared plus beta squared alpha plus beta whole squared minus twice of alpha beta So alpha plus beta alpha alpha plus beta whole squared money key and I believe I do alpha squared plus beta squared plus twice alpha beta minus twice alpha beta Okay.

[00:04:40]and I get it like a Q K money alpha into beta alpha plus beta value A Okay.

[00:04:53]alpha plus beta money key minus P minus P squared minus 1 or squared key plus 1 twice alpha beta money key twice Q So you do final answer. So second number two key this is alpha squared beta squared find out alpha squared beta squared So you do I mean that I get alpha beta whole squared alpha beta money key Q Q squared So you do So I might be say you have to alpha and beta are the more than twice X squared minus 7 X plus 5 Okay.

[00:05:36]If alpha and beta are the roots of the equation this then find the value of 1 by alpha plus 1 by beta and this 1 by alpha squared plus 1 by beta squared So I must do the key goal alpha plus beta will I know minus B by minus b by a money came alpha into beta 5 by Okay.

[00:05:59]minus b by a or c by a 1 by alpha plus 1 by beta is equal to I mean LCM alpha plus beta alpha plus beta 7 by 2 alpha into beta money came 5 by 2 So 2 2 cancel out of okay. So answer came 7 by 5 So question number 2 2 2 1 by alpha square plus 1 by beta square will have a receipt. 1 by alpha square plus 1 by beta square So alpha square alpha beta square So alpha square plus beta square money beta square plus alpha square I will come to alpha square plus beta square So alpha plus beta whole square same formula alpha square plus beta square came alpha plus beta whole square minus twice alpha beta alpha beta whole square So I will put color.

[00:07:00]7 by 2 square 5 by 2 put color So if they are mean I am p y q So let me So a two question of key question a two question a two 2021 what I say a two 2021 one of I say okay. 2021 2021 So if they are a two question I mean again I will come.

[00:07:32]So I will come again with this.

[00:07:33]question to come again Okay, observe color. one of the roots of the equation ax square plus bx plus c equation money came quadratic equation is equal to the nth power of other so they equal to the nth power of other.

[00:07:49]So, nth power Okay?

[00:07:57]Another alpha power n.

[00:08:00]of the other then find out alpha plus alpha power n when the alpha plus beta alpha plus beta alpha power n when the other roots to alpha power n.

[00:08:20]Okay?

[00:08:22]I mean alpha plus alpha plus alpha power n minus b by a minus b by a alpha into alpha power n is equal to k over c by a Okay?

[00:08:45]alpha power n plus one is equal to c by a Okay?

[00:08:54]So, alpha is equal [snorts] to c by a power one by n plus one over Okay?

[00:09:08]So, So, alpha I mean c by a one Okay?

[00:09:23]into alpha c by a c by a power one by n plus one plus a into c n plus 1 is equal to minus of b.

[00:09:57]1 minus 1 by n plus a by c is 1 by a power 1 1 by n plus 1 So I have c power 1 by n plus 1.

[00:10:11]a into a power minus of 1 by n plus 1 a power Okay. So the 1 plus 1 by n plus 1 So a into m into n formula 1 minus 1 by n plus 1.

[00:10:32]n plus 1 n plus 1 minus 1 So a power a power n i n a power n by n plus 1 i n 1 minus 1 plus 1 cancel out of minus 1 n plus 1 minus 1 1 2 2 cancel out of 1 n into c power 1 by n plus 1 plus a into a power 1 by n plus 1 by n plus 1 Okay. So I will multiply a power c power n by n plus 1 is equal to minus b.

[00:11:25]a [clears throat] power 1 and a 2 k a power minus n by n plus 1 a power minus n by n plus 1 1 n plus one minus one by n plus So it calculation So a power So one by n plus one common is one by n plus one plus a power a into c power n i will power one by n plus one is equal to minus b minus b So it is one Hello, hello I So I'm alpha and beta are the roots of the equation of this. Okay, come on then find out the value of this.

[00:12:30]So it will be okay.

[00:12:33]So alpha and beta or alpha or beta Yeah, they where I give up here. roots right So it's what So alpha or beta roots will equal to So they have alpha x or alpha beta direct put or it will be okay to get it. So alpha square it will be easier with to my alpha plus beta I don't know what I can So alpha square minus a alpha plus a plus b is equal to zero I will Okay. So alpha square minus a alpha minus k l minus of a plus b Okay. So it will be a two equation there. alpha put correlation Okay. So next it will be equation number one here. I will a two equation beta put beta put correlation beta square minus A beta plus A plus B So keep going to be by yourself.

[00:13:39]So A A 2 direct I mean hang it here. So you have to okay. A X plus A I will win.

[00:13:46]So A plus B is equal to zero.

[00:13:50]So beta square minus A beta is equal to minus of A plus B.

[00:13:58]So yeah, I'm equation number two D.

[00:14:01]So if you have to yeah Yeah, they put for left hand side the left hand side the So you have to put for one by A 2 equation where one by alpha square minus A alpha money key alpha square minus A alpha money key one by minus A plus B plus money minus I will have to you okay. one by A plus B Okay. beta square minus alpha beta money money you do alpha beta money to A beta. So A beta money key minus A plus B so minus 2 2 you have to money you have to key at the plus of Okay. So plus 2 A plus B 2 by A plus B.

[00:14:41]Okay. So you have to minus 2 A plus B I will go so you have to A plus B 2 common number 4 minus 1 minus 1 I will money minus 2 I will plus twice of A plus B.

[00:14:52]Okay. So you do you do cancel out of the like you have answer of zero.

[00:14:56]Okay. So they will be born at one of the quadratic equation of I don't know what to say. Okay. So first I accept that to complete after [snorts] that you have to have So you have to say so I can note down for So we have to get there.

[00:15:12]So A 2 2023 like say A 2 2023 days okay.

[00:15:18]So I love a question. Okay. I love a question.

[00:15:21]So you have to A 2 I will keep going.

[00:15:23]Can I keep going? If the product of the roots of the equation 82 equation Okay, if the product of the roots of the equation equal to the money alpha 30 added roots get the more alpha or beta the real life. You guys are So, alpha into beta equal to the roots of the equation equal to the sum of the squares of the money came alpha squared plus beta squared squared.

[00:15:49]So, question After that I'm going to keep going. If the product of the roots of this equation of this equal to the sum of a product to equal right car sum of the square sum money came plus Okay, squared money came take it out squared. Okay, so you can do this very very good. So, I mean you going to alpha squared plus beta squared minus alpha beta squared is equal to zero.

[00:16:19]Okay, so 82 again I will put in alpha plus beta whole squared minus 2 alpha beta squared minus alpha beta 2 alpha beta squared money came minus 3 alpha beta squared is equal to zero.

[00:16:32]So, alpha plus beta whole squared open modify the 3 alpha beta 2 alpha beta squared minus 2 You have this one. So, equal sign of this one.

[00:16:43]So, alpha plus beta money came minus b by a minus b by a whole squared Okay, 3 alpha beta money came alpha beta money came c by a c by a. Okay, So, you have money came a equal b squared by a squared b squared by a squared a formula came in here 3 c by a. So, a a a a formula came in here a a 2 a a 2 a formula multiply by a b squared is equal to 3 0 a c option b is correct. So, 82 question 3 4 82 Okay, then the value of this.

[00:17:42]Okay.

[00:18:16]Okay.

[00:18:33]8 is equal to Same as okay.

[00:18:58]Okay.

[00:19:03]5 by 8 minus direct direct some of the product some of the product money give alpha plus beta by the way the exam the key lab that tricks of the problem alpha plus beta money give minus B by A 64 64 by 1 alpha into beta money give 256 256 power is a 5 by 8 so if you have 64 give give my number two respect to two four two four 8 16 32 64 2 power 6 so 2 power 6 money give my number I mean 2 power 6 that's a 2 power 6 money that 64 128 256 128 256 256 so I'm going to give give me your number 2 power 8 5 by 8 so 8 8 cancel out what is 2 power 6 2 power 5 give me your 2 power 6 minus 5 money give me your number 2 so option B A is correct take this you can note down cool I don't have questions so what are you up to so in the 2021 2000 and 11 J W 11 so at the formula I am going to new money going so if you have if you question of the current money give me your number I am going to give you a call alpha plus beta is equal to any money give me your number number is over take this so that can be the option of that day so if you have tricks of money give me your number money give me your number Newton's formula take this so Newton's formula money give me your number so if you have money money give me your number okay Newton's formula Newton's the the SN is equal to alpha power n plus beta power n the other thing.

[00:21:15]Plus minus, okay? Alpha power n but minus plus minus z the other thing is beta power n again I have a two the equation any car any car formula money come from Newton's formula is probably going to be happy, okay? Basically easier to do that. The TT are I mean it will be a problem. I'm a condition that is no SN is equal to alpha power n plus beta power n. TT I mean it will be a problem or a into SN plus b into SN minus one plus c into s n minus two is equal to zero. A to the property of one or two here.

[00:21:51]You guess it.

[00:21:52]So zero is a Newton's formula Newton's of 20. I don't get it a b c q a a x squared plus b x plus c coefficient get out of it. Okay? So you have to do more a a two line Our past time to get it n plus one second time to get it third time to get it n minus one. It is the I mean SN n plus one put quantity I'm going to be able to do this to because it's why you have to pay attention to follow what it says. A into SN the next time to do it again and again come here with it. I don't know the next time to do it again and again I don't know the time to do it again. I know. So n plus one only a into a s n plus one only plus b into next time to get it to do it again and again.

[00:22:35]SN n plus one minus one I don't know what it is.

[00:22:39]SN I don't know what it is. So plus c into s into n minus one I don't know what it is time to Okay? So if you want to keep going to do it again and alpha SN money alpha power n plus one plus beta power n plus one put question I mean What is that?

[00:22:56]So if you want to do it again to follow follow what it says I don't know what it it is going to be coefficient or look at the target SN two a S So, option A is correct.

[00:23:28]If alpha and beta are the roots of the equation of this, okay? So, with alpha is greater than beta if A N is equal to alpha power N minus beta power N. Okay? For N greater than equal to 1, then the value of this.

[00:23:44]Okay?

[00:23:45]>> [clears throat] >> Alpha power N minus beta power N.

[00:23:52]So, So, the number You have to Then Then I A 10 put here to give alpha power 10 minus beta power 10.

[00:24:17]Okay?

[00:24:18]So, A 2 equation So, our Newton's formula gives A into S N plus B into S N minus 1 into A. C into S N minus 2.

[00:24:35]So, 1 I give up.

[00:24:38]I might A A So, A 10 minus It is plus minus You have to You You Okay?

[00:24:57]>> Okay.

[00:25:02]Okay.

[00:25:11]B Okay.

[00:25:18]A into C C value 2 0 0 So Okay.

[00:25:51]Okay.

[00:25:54]minus Okay.

[00:26:02]divided divided Okay.

[00:26:09]divided Okay.

[00:26:24]Okay. The final answer is C.

[00:26:26]Clear.

[00:26:27]Okay.

[00:26:29]Newton's Okay.

[00:26:32]Okay.

[00:26:36]>> [snorts] >> So So 2021 2021 Okay.

[00:26:51]So easy So So, x minus lambda is equal to our x minus four is equal to one yes. Okay? So, so a equation to zero look better than you can make. Tomorrow the first of the key of zero look at the key of one. Lengthy process of but we will open it. Okay?

[00:27:12]Into what is the easier method going to say yet yet the two case going to open it. Okay? So, So, key key case going to open it. A equation [clears throat] to one key to the one.

[00:27:21]The key to the two number one of them. I know.

[00:27:25]A one over like you want over like first case. Second case to key over two time minus one over like.

[00:27:31]Okay? So, minus one minus one into minus one key over one. One into one money key over one. The key at the minus one I want to be any good one minus one one into minus one money key over one.

[00:27:43]But one I want equation to satisfy no so a to the condition I get this by one.

[00:27:47]Do you get it? So, one I want to be any good condition of this so two days over the sum.

[00:27:52]The first case over the one.

[00:27:55]First time I do x minus four is equal to one. Okay? So, x over the one key over five. Okay? So, if you x minus lambda is equal to key to the one.

[00:28:06]According to first condition one and one over one.

[00:28:09]So, x over the one key over one over five.

[00:28:12]Five minus lambda is equal to one.

[00:28:14]So, lambda is equal to four.

[00:28:16]Okay? Lambda to be one and one to be one and one. Minus one means four.

[00:28:21]So, if you have two number condition two.

[00:28:25]So, lambda to be one and two four over like into I don't know but check for this minus one over like one and one. So, x minus four is equal to one put minus one put three. Okay? So, x minus four is equal to minus put three and x over the one key over minus one and four to be one and one over three and so if you have x minus lambda is equal to K, minus one. So, X X X X X X or value K lambda 3 minus lambda is equal to minus one.

[00:28:54]So, lambda value K I will follow you.

[00:28:56]So, upset A is correct.

[00:29:00]So, it is a common important question.

[00:29:03]Okay, so it is a quadratic equation or or sequence and series mix mix mix question. You guys are So, if A B C and X are non-zero real numbers are imaginary numbers. And then A square plus B square X square whole A condition if it take a bonus if it take a bonus if it take a bonus if it take a bonus if it take a bonus if it take a bonus The solution K A will So, if you want to keep going discriminant is equal to zero lower Okay, so discriminant is equal to zero lower lower lower lower A square plus B square minus 4 AC not twice B into A plus C whole square A beta minus 4 into AC 4 into A square plus B square B square plus C square is equal to zero.

[00:29:55]If this is equal to zero I can learn more. Is equal to zero I can learn more.

[00:29:59]Current AP is equal to H speed condition satisfied or you will like it the equal of the like you have there.

[00:30:05]Okay.

[00:30:08]Is there any case that you have AP take it on keep on going twice B is equal to A plus C keep on going if you have GP take it on keep on going B square is equal to AC keep on going Okay, H speed take it on you are a winner if you are a winner winner winner winner winner winner winner winner twice B by A plus C I think it is any question.

[00:30:29]So, if you have the 4 B square if you have the beta of K beta square plus C square plus twice AC minus 4 A square beta beta beta minus beta beta beta 4 A square B square Okay, minus Okay, minus 4 a squared c squared.

[00:30:53]Minus 4 a squared c squared minus minus 4 b power 4 minus 4 b power 4 minus 4 b squared c squared is equal to zero.

[00:31:14]So 4 b squared a squared plus 4 b squared c squared plus 8 b squared ac.

[00:31:26]So >> [clears throat] >> minus 4 a squared b squared So the kiki cancel 4 b squared a squared 4 b squared c squared a 2 a 2 10 cancel out.

[00:31:43]Okay, so basically key 8 b squared ac minus 4 b power 4 minus 4 a squared c squared is equal to zero.

[00:32:03]So if you are okay 4 b plus 4 a squared c squared I will minus 8 b squared ac is equal to zero.

[00:32:23]So if you are 4 b power 4 twice b power squared plus 4 a squared c squared k k k k k k k twice of ac whole squared minus twice of ab first time a plus b whole squared twice of A into B equation twice of A into B A money A to B money A to twice of A money twice B C money key twice of AC B money key money twice of AC twice of AC So >> [snorts] >> But you have to twice B square whole square you know twice B square whole square So you have to B square that I will B square to you have to you have to modify what you have you have to square you have to B square Okay, is equal to zero.

[00:33:16]So if you have to have A to A so so two two four eight eight B square AC has a lot of I see So if you have to twice B square minus twice AC whole square I will is equal to zero I will So if you have to square root take care twice B square twice AC to different ratio twice of AC So B square is equal to K AC So what they will do here GP take care come home So you can note down here I mean I will put something So what they have to have A to A to question I think C W I think power of two A to J W 2019 J W means what I say Okay, 2019 J W So if you have to have some money get a question J W question A to last C W lucky money J W question Okay So you have to give what you say The probability of the roots of the equation of this are real real money you have to have thinking you have to you can have to take care real money you have to have discriminant greater than equal to zero okay that are condition you have to N belongs to N N less than equal to five probability take care So if you have to have B square minus four AC it will give you b squared minus 4ac.

[00:34:39]Greater than or equal to zero. B squared into quadratic equation n squared minus 4 into a into c a minus 1 c minus n by 2.

[00:34:49]Greater than or equal to zero. Okay? So, n squared minus 2 2 by 2 times double. I don't know greater than or equal to zero.

[00:34:58]So, n common get the n minus 2 okay greater than or equal to zero. So, the army real our condition n is less than or equal to five. Okay? So, natural number n belongs to n belongs to n belongs to n so it is a n belongs to n get the out.

[00:35:18]Natural number start one or start you get it. So, n is equal to possible condition 1 total condition total total.

[00:35:29]Okay? So, possible condition possible.

[00:35:32]I don't know probability possible so it will be a method okay in depth I don't know so first one put one into one minus 2 minus minus 2 zero I don't know so you satisfy nobody.

[00:35:49]Okay? So, one satisfy nobody so I don't know possible so 2 2 minus 2 zero zero I don't know equal sign so 2 okay so 3 over 8 2 3 2 3 4 5.

[00:36:06]So, total number of outcomes probability probability probability probability.

[00:36:14]So, total 5 times 6 total natural number n less than or equal to 5 5 so condition 5 so 4 by 5 option d is correct.

[00:36:27]So, it [snorts] is a double I say I don't know how to so I come concept can you connect with that in that concept number of integral value of M for which the equation real roots real roots I sorry no real roots no real roots money key imaginary roots of 110% b square minus 4 AC less than zero okay so b square money 2 into money to b square of 4 is a ball 1 plus 1 square money 1 plus 5 m square money a term 2 square b square money 820 square so 2 square 4 a square plus 9 m square plus twice a b money 6 a money okay minus 4 into AC 4 into 1 plus m square into 1 plus 8 m the direct coin 1 into 1 1 plus 1 into 8 m 8 m okay m square into 1 plus m square m square into 8 or borrow 8 m cube so less than zero so it take care you 4 plus 36 m square minus 24 m minus 4 plus what is the minus I tell you what what m plus minus minus 4 m square minus 24 I 24 32 m cube less than zero 80 a 4 + 4 cancel 36 m squared and squared and 36 m squared minus 40 4 m squared minus 32 m squared plus 24 m minus 32 m given a 24 minus 32 minus 0 68 m i Okay, so minus So minus 24 m 36 m cubed and 82 and last of 36 m cubed less than 0 So 36 20 So you have to give 36 36 minus 32 minus 4 and 32 m squared able minus I don't 24 m minus 32 m money 8 m i okay minus 32 m cubed less than 0 52 a woman What do I have to take over 32 m cubed minus 32 m squared plus 8 m So you have to minus 8 multiply 20 to 7 So you have to 8 at the common law m at the common law So you have to answer the one but this 4 m squared minus 4 m plus 1 greater than 0.

[00:40:24]80 80 divide m into m into twice m squared 1 twice m minus 1 whole squared formula twice m minus 1 whole squared greater than 0. Okay?

[00:40:43]So it just a number number line of put color Okay? Number line of half I go out there.

[00:40:51]Half I go out 0 I go.

[00:40:54]And the half of the demand the one number that put color pass color positive or I go I go six put color positive or I go I go. So if I write key positive demand the one number put number positive I go go human get a number for a moment more I know. So infinitely many solutions okay.

[00:41:14]So in the note down color here I will write down my work by So what do you have to have a good question right now? In 2015 data in 2019 data data So you do question right now you have to work in the concept for my sake here is a So you do question now.

[00:41:32]So you do part of very very good to me exam ready person to get a 32 question by itself.

[00:41:37]Okay?

[00:41:38]So here I have to have a good question you do question of two you do I mean questions of two So if one of the roots of the quadratic equation of this is cube of other okay? Then the value of k. [clears throat] K value will be same.

[00:41:58]So you have to root the alpha right?

[00:42:00]Another root to give a alpha bar cube.

[00:42:02]So product of the roots give away at the 256 by 81 So alpha bar 4 is equal to 256 or I can write it as to 4 ^ 4 ^ 4 81 I can write it as 3 ^ 4, okay?

[00:42:24]So, alpha value can be plus minus 4 by 3.

[00:42:31]Square taking the head plus minus I had 4 taking the cure. I don't know why. Alpha ^ 4 to the alpha square whole square taking the power of the even number taking the even number taking the total value of the Okay.

[00:42:49]For better understanding the total value of the So, alpha plus alpha ^ n money I'm not kidding I have to say minus b by a minus b by a minus k by 81 Okay. So, alpha money I'm not kidding I have to say 4 by 3 Wait, it's 3. Alpha cube.

[00:43:14]So, 4 by 3 4 4 by 3 taking the same So, 4 by 3 plus 4 cube by 3 cube is equal to minus k by 81. So, I can put it as well.

[00:43:32]So, 4 by 3 common value of 4 by 3 over k 1 plus 4 square minus 16 3 square minus 27 3 square minus 9 is equal to minus k by 81. 3 the 81 of 27 times of all It will cross multiply for either I can calculate for all. K value of all minus 300. Do you have to calculate for all of the mixer for So, 82 2019 data will be very much important money more money important money more money I don't know what to say, okay? So, if you have to question I can solve for you.

[00:44:10]>> I'm working on this concept in my head.

[00:44:11]Okay.

[00:44:17]So, alpha beta are the roots of the equation of this equation. Then the least value of n for which alpha beta power n is equal to one.

[00:44:31]So, x is equal to minus b plus minus under root of b squared minus 4ac by 2ac.

[00:44:36]So, two plus minus b squared minus 4 4ac minus 8 two over two plus minus two under root of minus one minus twice of iota two minus one plus minus iota one plus iota over alpha or one minus iota over beta two is equal to Okay.

[00:45:21]I mean I can hear you.

[00:45:23]complex number iota under root of minus four under root of minus four four into under root of minus one over under root of minus one iota four under root of four two Okay.

[00:45:37]>> [clears throat] >> alpha by beta Can you hear me over there?

[00:45:41]So, theta is equal to tan inverse of one by one Okay.

[00:45:49]So, tan inverse of one one by one pi by four one plus upon in depth concept to my head so focus one plus iota a two a s d c more trigonometric So, ASTC into imaginary axis into real axis So, 1 {comma} 1 So, first quadrant of pi by 4 and 1 minus iota beta theta here tan inverse of minus 1 by 1 minus pi by 4 angle So, into quadrant of 1 {comma} minus 1 So, minus pi by 4 to 1 to 1 to 1 to fourth quadrant fourth quadrant of tan Q negative of Euler formula e power i theta is equal to cos theta plus iota sin theta Euler formula I mean here to done and it will be going to put on me Yeah, but it will be 1 plus iota and 1 minus iota whole power input core It will be out of the way then.

[00:47:33]I know.

[00:47:34]It will be out of the way then. 1 plus iota and 1 Yeah, 1 plus iota and 1 minus iota by 7 1 plus iota divided by 1 minus iota That's what the rationalized formula rationalized formula 1 minus iota 2 by multiply by Okay. So, if you are more than 4 in a row you have to Yes, I will. one one one one one one one one one one one one one one one one one one one one one one one one one one >> Doesn't matter.

[00:50:03]Okay, I don't know.

[00:50:13]So, I do what?

[00:50:15]So, I don't know what you said.

[00:50:20]Then, this I'll find out.

[00:50:23]So, Yeah, I don't know.

[00:50:30]Omega 3 I don't know.

[00:50:35]complex number So, yeah, they are Omega 3 one minus 101 plus minus omega power 10 7 What minus 2 common level omega power 101 plus omega power 100 7 day minus 0 omega square plus omega 101 I don't know what you are doing.

[00:51:27]3 minute divide by 6 square So, 3 minute divide 3 minute divide 2 You got an omega square.

[00:51:48]omega power 33 into omega square. So, omega power 3 omega power cube omega cube money one So, open up the money power not out. Open up the money power not out. Keep it here. The one to keep out. This stuff could be one power three 33 money one area So, they can omega cube money one area into omega square Lucky out of the omega liquid. A two can get omega cube deeper and thing to divide Korea so no. So, it don't hold up. Don't you divide Korea? It will put Korea deeper.

[00:52:24]I remind you the demand regular.

[00:52:26]It will do the logo omega rotator. No idea. Yeah, the dollar 30 regular 30 regular 50 regular 50 regular No regular 50. Next to next to it.

[00:52:35]remainder to your home 50 30 divide Korea remainder to your home maximum 30. Okay.

[00:52:41][snorts] So, minus omega It is what? omega plus omega square money give money money minus one area so omega plus omega square area to apply area to apply one to give a little bit here minus one omega plus omega square minus minus plus area to So, one is the final answer option C is correct.

[00:53:07]Okay. So, option C is correct. So, it here it will go somewhere to try to go.

[00:53:12]I don't know what you are saying.

[00:53:14]I don't know what you are saying. I don't know what I don't know what you are saying. I don't know what you are saying. So, what you are saying So, x square minus 30 kx You have no one modify what you want.

[00:53:23]Product of the sum of the equation of this is Product of the sum of the equation of this is I don't know what you are saying. I don't know what you are saying. I don't know I don't know what you are saying.

[00:53:32]So, what you are saying So, 30 kx So, you have You have to do what I say.

[00:53:37]Okay. So, A two and a open up the money get open up the money Okay. So, twice into k squared minus one is equal to zero.

[00:53:46]Fine?

[00:53:47]So, x squared minus twice kx plus So, if there's a k squared or you have the base same as it If there's a e here, you have the e derivative. If there's a 10 here, you have the 10 derivative. These are beneficial. So, if they are not here, these are beneficial.

[00:54:01]So, you have the same as the same here. You have the same as the same here. You have the log two to the right. That is k or twice of k squared minus one is equal to zero.

[00:54:09]So, you do the property of logarithm, boy. You see the base of logarithm.

[00:54:14]So, you have a k able You have the So, you do to see over here. Product of the roots give this a lot.

[00:54:20]Alpha into beta gives a seven.

[00:54:22]Then the roots are real.

[00:54:24]Are real volume of this equation.

[00:54:25]So, I'm a k d s a Alpha into beta money k d s a seven So, alpha into beta money k c by a money twice k squared minus one by one So, twice k squared minus one zero is equal to seven.

[00:54:41]Uh so, twice k squared is equal to eight So, k squared is equal to four two to divide over. So, k value k here. Plus minus four Okay?

[00:54:56]So, plus minus four not two.

[00:54:59]So, minus of the answer not. So, plus two is correct answer. Okay?

[00:55:02]>> [snorts] >> I don't follow real.

[00:55:06]k value the greater than zero a b squared minus four a c is greater than zero.

[00:55:13]So, if you need over If you have a little question of tomorrow of them Take it out question query bar. I wish I could get the sector of tomorrow confidence I could say. So, if you have a total of four So, keep out of quarantine and I guess I do lecture to say. Very very good.

[00:55:30]So, they have the end of the question query in the video. I was going to do the question query video. It is a double the hour question so I get it.

[00:55:37]I should have I would like to get this lambda So I will list find out okay So it the equation to I will modify with that I can name So extra So you have to give x square plus 3 minus lambda x plus 2 minus lambda Okay.

[00:56:06]one day to day So least value find out the value of some of the squares of the roots square of the roots money can offer square plus beta square and alpha square and beta square then the least value is alpha square plus beta square and minimum value alpha square plus beta square alpha plus beta whole square minus twice alpha beta alpha plus beta money can minus b by a and 3 minus alpha minus b by a whole square I will minus of minus of minus twice alpha beta c by a c by a 2 minus alpha 2 minus alpha Okay.

[00:56:56]So if you are you have to give a 9 plus lambda square I will 9 plus lambda square I will minus 6 lambda minus 4 plus 2 lambda So if you are 9 plus lambda square lambda square lambda square that side of lambda minus 6 lambda plus 2 lambda minus minus 4 lambda Okay. So I will take a lambda 9 minus minus 4 money can plus 5 Okay. So lambda square minus four lambda plus four plus one one and one least least a good deal for us to get the list of the lambda zero lambda 2 over the lambda is equal to two over a good thing in a very good 2 minus 2 whole square plus one.

[00:58:00]Okay, at least one two minutes minus three minus minus three minus three minus two whole square whole square minus five whole square plus one 25 plus one minus 26 80 minus 2 is equal to positive square so it you have to and I get okay so you can lambda lambda lambda lambda 221 and you have to eat optic okay so option B is correct so equation equation equation equation 51 equation x square minus alpha plus beta minus sum of the roots plus product of the roots is equal to zero is the equation from here so sum of the roots x square minus 2 into 8 minus sum of the roots into x plus product of the okay better so thank you again okay so bye bye good night take care sweet dreams and all that very best