How To Solve An Octic Equation? | Solving Amazing Octic Equation | Aman Sir Maths
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- Опубликовано: 22 янв 2025
- In today's video, we will be solving an octic equation - 2x^8 - 9x^7 + 20x^6 - 33x^5 + 46x^4 - 66x^3 + 80x^2 - 72x + 32 = 0
You must be wondering that till now in your syllabus you have learned to solve equations up to power 4 but this is an octic equation ie. power 8.
How will you solve this equation?
Give it a thought and apply concepts that you learned to solve an equation of power 4.
If you are unable to solve it, let's check out how Aman sir will make this complex octic equation very easy to solve.
Check out the complete video to know the solution to the octic equation.
Subscribe to @BHANNATMATHS for brain-twisting videos around maths.
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Sir mazaa aa gaya.. this is one of the best questions I have ever solved… sir please bring more videos like these.. I really love your videos 😊😊
Me : it's scary
Sirji : it's beautiful ❤️💕
facts bro
Sir you are brilliant 👍😎 and your teaching style is very unique to all 🙏🙏 you are legend sir 🤓🤓
😎😎😎
👍👍👍
Sir last me mja aa gya. Bilkul bhannat tarike se.
Sir really maja a gya first time mathematics ki itni large equation ko solve karnai mai so love you sir for that struggle
Sir please start teaching us BSc and engineering mathematics it will help us a lot. your teaching style is so unique sir🙏 when I was in 11th and 12th I studied maths from your videos and I always love to see your videos sir your all videos are amazing and loving.🤍♾️🙏
so what we did is we converted fractional expressions to reducible forms so that it can be easy for us to solve. nice
❤ really love your videos sir,,,plz ese video laate rahiye jisme question ki approch discuss ho..❤
Sir its very kind of you to help us for so long without any charge
Bohot accha samjhaya hai aapne 🔥🔥
There are Mathematics channels like 3Blue1Brown, Mathologer, Black pen red pen, etc in RUclips. This channel can become a popular Mathematics channel from India as Sir looks interactive when teaching
Only if sir teaches in english
@@TechnoCoderz369 why english. Why can't we have channels like 3Blue1Brown, Mathologer, Black pen red pen, etc in hindi
@@amits4744 Because not everybody knows Hindi🙄
@@amits4744 Hindi is not a universal language so that is why we should speak in English
@@amits4744 entire world uses english. Its not anti-patriotism for you to accept this fact😭. Indians really be defending India in everything lmao
Zeher sir maja aa gaya mujhe toh bahut mushkil lag raha tha lakin aapne ekdum easy way mein samjha diya
Kya kabhi koi dusra questions kar paoge?
@@MathematicalPool of course agar isse similar hoga tab kyon ki 10 wagera mein maximum power 4 tak hi questions padhaye gaye hai
@@dragonslayer7364 10th me 4 degree padh liye ho???????? Kaha se ho bachche??
5:42 amazing dance 😂😂😂😂😂
1 is a root
As sum of coefficients is zero
Mind blowing 🤯😲
Best teacher ever sir!!
I WOULD LIKE TO SUGGEST A SMALL THING 👉🏼👉🏼
Sir ऐसी वीडियो बनाने से पहले इसे COMMUNITY टैब में पोस्ट कर दिया करिये लगभग 5-6 hours पहले 🙏🙏🙏
Learned something new sir ♥️♥️♥️
Sir I love you, u r my inspiration 😊🙏🙏
Fantastic Sir love you sir ❤️
Sir outstanding.🙏🙏
Sir mujhe itne achhe lagte ho ap kya hi bolu main . Mera fav sub bhi mathematics hai . Isliye main apka har ek video dekhta hun kuch neya sikhne ka liye
5:43 Sir aa gayi baat samajh mei :)
Sir I have a request.. please make a video on 'Descartes Rule of Sign'.. please sir, before JEE starts 🙏
Very easy question tha sir..❤
Amazing problem sir! Than you so much ❤👌👍
You can use pascal triangle for roots of t atleast
quadratic equation❌
Kudratic equation✅
You ar amazing sir.❤
Sir u r amazing sir
Hit and trail method ko chhod kr kya koi dusra method n use kr skte hai?
How to find the height of any triangle when side length is given. I mean that if any triangle's side is a, b and c then what will the height be of this triangle.............🤔. Is there any formula, by using that we can find the height of any triangle........
Find the area by herons and divide by base
Sir isko x - 1 se divide karke bhi solve kar sakte the na?
Sir ye to ek dum starting mei hi hit and trial se ho raha tha maine bhi pehle 1 daala phir 2 aur ho gaya solve. 1 minute bhi nahi laga. Maana x=2 ki calculation bohot heavy hai par phir bhi ek baar calculation karlo to bohot jaldi solve ho raha hai pura question.
wait but this only works if you assume there are real solutions which doesn't always work and isn't general.
Very nice problem
Sir, do we have any simple solve of octic equation like quadratic one.
Reciprocal equation
Thanks a lot
Sir thank you for the great explanation,
As you said to solve it yourself once, so i tried it , i got the one value of x that is (1)
Sir : app video pause karke apna attemp lagaye
Me : mera attenpt toh thumbnail dekhke hi pura ho gaya tha
Love you sir❣️
Sir please start class 11 maths. Our board exam was over
Sir aap amizing videos ki playlist bana do na please
Sir aur koi condition ya coefficient pe octic equation solve kareya kyoki
Iska 8 Zeros ayega
Aur sir aise question ko put up kariye jiske zero irrational bhi ho
Trial and error with x=1, and x=2 can be tried just after dividing by x^4
but how will you find other roots? for that you have to reduce it to a 4 power equation
very very nice equation I loved this equation a lot
Legend of mathematics
How did you know after changing octic equation into biquadratic, trail and error will give you a factor of it. Why didn't you try x values in the beginning only as all the coefficients of x were integers only.
Isne question ko khud se set Kiya hai ki easily solve ho jaye nahi to mai challenge karta hu ki bas thoda sa change kar dunga aur solve karke dikha de .Mai challenge karta hu nahi kar payega.
@MathematicalPool be respectful to sir
Sir function x²+2x+1/ x² - 8x+12 ki range Bata dijiye
|R\(-21/4,0) ?
I saw every video .. That's done by u
Wow 👍👍 ❤️
Sir app insanely nahi devta hai devta❤❤
Live you sir you are legend
Sir aap x^4 se divide kar rahe hai both sides. Aisa ham tabhi kar sakte hai when x is not equal to 0. Aap ye chiz nahi bataye video me.
So first we should check if x=0 is a solution of the equation or not.
If x=0 is a solution then how can we solve this type of equation by this approach? Please tell me.
Sir please teach us BSC SHM Chapter too, it's proof are kinda complicated, but if you teach it, then it will become so easy!!
Sir please one shot videos banaiye for jee
Sir kya yah har bar hota h ki agr base same rahte hai to power ko equality me compare kr sakte h?????
Kyunki agr aisa hai to 1^1 =1^0 me 0=1 hojayega
Let's see
Suppose a^n = a^m
So a^(n-m) = 1
Now take log of both sides,
log a (n-m) = 0 ( log of 1 is 0)
either
n - m = 0
n = m
Or log a = 0
a = 1
Conclusion, for the no 1 and only for 1, m might not be equal to n.
Hope ,it helps
That rule is valid when base is not equal to 1.
very nice.❤ I am from Bangladesh
Sir please launch app for jee mains and advance 2024 for math please sir
Sir why dont you start math olympiad series
you are the gret
Sir please bring jee advance toughest questions
Sir please differentiation class 11 PE ek series bana dijiye na. AAP ke channel me class 11 differentiation pe koi vi playlist nhi hai aur aap se parne ke baad aur kisi teacher ka lecture accha ni lagta hai
To be honest As a MSC maths
I could easily tell that solving every octic isn't possible
Is it bcz QUINTIC EQNS KA KOI FORMULA NHI BANA BS QUARTIC KA HOTA H JO KI MERE TAK KO BHI SMJHNE ME HALAT KHRB HOGYI NO ONE USES IT ...ITS TRASH TBH😂😂😄🤣🙂😑
Neither is any equation with degree of polynomial more than 5
(Only possible if u use computer)
@@e_pi_i_is_-1Galois Theory
@@e_pi_i_is_-1 bhai bhai 5th ka bhi formula nhi hota bro or aage ka to bilkul nhi
@@Reeta78909 you can deviate the formula just like u deviate the formula for quadratic equations.
Only thing is that, it would take up like 10 pages of register.
The cubic formula takes one a4 sheet
@@e_pi_i_is_-1 ye proof ho chuka hai 4 degree ke baad aap solve nahi kar sakte hai
Sur, you are freat !!
Olympiad ka batch hai to bataiye n sir 🙏🙏🙏🙏🙏
Sir yea to reciprocal equation
What if we apply contradiction method on √9 ?
My answer is coming irrational but we all know that it is a rational number.
Then what fundamental mistake is done while applying contradiction method on √9 ??
There is a theorem in which if p is a prime number and it divides a^2 i.e. p is a factor of a^2 , then p divides a also i.e. p is also a factor of a.
When we proof √2 irrational , we get p as 2 which is a prime number and therefore we can apply this theorem and proof that √2 is irrational .
But when we do this with √9 , we get a equation 9b^2=a^2
Here , p is 9 BUT WE CAN NOT APPLY THE THEOREM BECAUSE 9 IS NOT A PRIME NUMBER.
Since we can't apply this theorem, we cannot prove by contradiction that √9 is a irrational number.
Therefore, √9 is a rational number as we all know.
HENCE PROVED
There is nothing wrong with maths, sometimes we just don't know how to apply rules.
Sir I have a doubt
Sir linear equations me x ki 1 value aati hai
Quadratic me 2 aate hai
To octic me 8 values aane chahiye n ?
🙏
Yes ,
8 values mai se 2 values hai jo REAL hai .
Baaki 6 values COMPLEX NUMBERS mai ayegi .
Sir ne nhi nikali hai , aap nikal sakte ho is formula se
-b±√(b²-4ac)
______________
2a
Jo bhi Aman sir ko pasand karta ho like karooo❤❤❤❤❤❤
Sir ji x+2/x ki seedhe range se pta kr sakte hain ki soln hai ya nhi .Range by am gm (-2√2,2√2 ) me non real
जय श्री राम
I LOVE YOU VERY MUCH SIR 💟 💟 💟 💟 💟 🤗🤗🤗🤗🤗🤗🤗🤗
Sir please make video on geometry new concept
Super 👌
python produced 8 solutions of this equation {1, 2, -3/4 - sqrt(23)*I/4, -3/4 + sqrt(23)*I/4, 1/2 - sqrt(7)*I/2, 1/2 + sqrt(7)*I/2, 1 - I, 1 + I}
Bro, who is python
Sir GOD OF MATHS 🥶👺
If it is asked how many total solution no matter real or imaginary what would be the answer??
8
5:43 bhannat sir is dancing
Machhli jal ki rani hai
Sir aise kitne equation hoti hai
mene starting me x=1 put kia aur vo satisfy kia toh long division krke Quotient nikall lia first attempt me
Sir aap physics ka koi bhi topic khud se padhaiye naa 🙏🙏🙏
Sahi baat hai bhai uss field main bhi Ratna kam ho jayega aman sir ke ate hi
@@mathmagic8577 physics me ratna padh rha hai bro to bahut weak hai fir
@@divyanshdixit3445 achha,according to bohor L=nh/2×3.14 ye kaise proof kiyq gaya kuch padhate hai sidha bol dete hai Harare yaha agar tumhe samjme ata hai to bhaut badhiya baat agar nahi ata hai to tum bhi rat hi rahe bhai 😄 baki tum samjdar ho hi
@@mathmagic8577 bhai dekha jaye to ye chemistry ka hota hai par physics me bhi dediya hai aur chemistry ka to sabko pata hai ratna hi padta hai mai core physics ki baat kr raha hu like mechanics, waves ki baat kar rah hu agar usme ratna pad raha hai to weak hai aur ye jo hai vo bohr ne hypothesis kari thi to uska koi proof hi nhi hai to derive kaha se hoga
@@divyanshdixit3445 bhai yaha par Maine core physics nahi bola physics bola aur tumne bhi core physics nahi sirf physics ki baat kar rahe hai
Me direct hit nad trial method
Sir please make video on Taylor series
Sir u r fire
Sir, I have a little question 🙋♂️
Why does this octic equation not follow the Descartes Sign Rule? According to that.. It must have 8 positive real roots... But, it only have 2 real positive roots!!
If you kindly explain... I will be highly obliged🙏
Please sir... Kindly keep my request 🥲
it is because the descartes rule states that the MAXIMUM no. of zeroes can be equal to the no. of sign changes, it does not say that the no. of zeroes has to be always equal to the maximum possible. the descartes rule says that maximum can be equal to no. of sign changes, so we have for this equation maximum as 8. but another possibility is 6, or 4 zeroes, or 2 zeroes.... or even 0 positive real zeroes. but we calculated it as 2, so we know answer is 2 positive real roots.
abey The degree of the equation= the number of roots
Iske 6aur roots hai par woh complex roots hai toh unhe sir ne consider nhi kya
@@syed3344 Politely talking to you.. Kindly go through my comment once more.. Kindly understand what I meant to say & don't be oversmart🙂
@@swarnavabanerjee6908 lodu oversmart kon ho rha hai
@@syed3344 Typical psycho!! I think you should contact a psychologist 🙂 because you can't comprehend what I said
Sir ek inequality series layiye ❤
Are these zeros coinciding? because ideally an octic equation should have 8 zeros right?
An octic equation must have eight zeroes but,they need not to be a real numbers as a solution
In this octic equation,there are only two real solutions and the remaining six are unreal solutions
@@saraswathygopal3322 so why would the graph look like?
@@chiragbulbule The graph will intersect only at 2 points on x-axis
Maine solve Kiya and 1 aya
sir phir se kbs show kijiye na
Sir jee mains pe 75 %criteria lag gaya hai sir
When I need to solve this question, I always use 1 -1 and 0 even 2 and -2 , so I can 'explode' the quotation instantly😂
Mene bhi same steps kiye the par beech me calculation mistake kar di🥺🙃
Ram ram ji 🙏
bruh i struggle with cubic and hes doing octic😐
Namaskar guruji
Maja aya
❤🔥🔥
This js extremly extremly rare case 😂
Not possible irl
Only possible if the question is rigged to solve like this 😅
x = 0
done
phir bhi galat hai bro
x=1 is correct
Ye kya tha 5:40 se 5:45 🤣🤣