Discriminant of quadratic equations | Polynomial and rational functions | Algebra II | Khan Academy

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Discriminant of Quadratic Equations
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Опубликовано:

11 сен 2024

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Комментарии : 183

@CrazyNateKosty98 9 лет назад

I gotta give it to you, I learned more from you than my teacher

@NeekoKid 7 лет назад

Nate Kosty lol my teacher tells us to watch this guy

@kkngenomesho7744 7 лет назад

if she knew him, theyd prolly marry each other

@andrewolseen3416 6 лет назад

Nate Kosty sameeee

@lancestephenson2977 6 лет назад

Nate Kosty i know right

@edgelalarcon1490 6 лет назад

Edgel Alarcon go

@skuffd-semicolon 5 лет назад

The amount of OOOOHHHH!!!! moments I had after watching this.......

@sayloraks9334 3 года назад

Wow. Thanks for making me feel bad. I had none😪

@FishNugget-we9oi 3 месяца назад

@@sayloraks9334other people learn differently it good to let those who dont know to learn

@crazyloco97 11 лет назад

I learned in 2 minutes of this video what took me 1 hour in class to get confused over

@anaisperez2704 3 года назад

same

@todayjanuary2012 12 лет назад

My teacher: ***stacks piles of papers on my desk*** DO IT! You: OK... Let's go over this slowly YOUR THE BEST!! I ACTUALLY UNDERSTAND WHAT I'M DOING IN MATH CLASS NOW!!! :D

@nojam4988 2 года назад

2021

@Ineedaname-ym2bo 3 месяца назад

2024

@musiciseverything333 11 лет назад

Thank you dude! I fell asleep in class. Watching your videos are going to help me get through Algebra 1.

@aucool7869 6 лет назад

khan academy just makes my life easier. My teacher makes everything all complicated but Sal just makes it simple and easy to understand. THANK YOU KHAN ACADEMY

@tazreenkhan4890 3 года назад

Deciding to watch this video is one of the best decisions I ever took in my life.

@codingwithkenny6492 3 года назад

Sal is the best math teacher in my opinion. He simplifies the mathematical computation and makes it much less confusing than most Math teachers.

@ashaa.5616 8 лет назад

oh my god, thank you so much for this because math has not been life.

@colemanroberts6827 8 лет назад

+Asha A. crystal castles!

@randomfandom33 7 лет назад

mmmmmm... saying "oh my god" is technically blasphemy

@glnpy 5 лет назад

@@randomfandom33 be quiet

@futurine8197 6 лет назад

Every time I finish a video is like "this is so easy how did i not understand it before"

@Flameplaysofficial 7 лет назад

I learned more from you than my Teachers way less confusing

@loversjustkeeploven 13 лет назад

Aced my final. thanks breh! u saved me from military school.

@balqisaadan8132 3 месяца назад

how old u now

@samsungsaiyam1090 3 месяца назад

RIZZ

@balqisaadan8132 3 месяца назад

@@samsungsaiyam1090 hshaahhaah u wrote that comment 12 years ago, I was js wondering

@liquidsmoothgrr 4 года назад

Watching this because my teacher got mad and she didn't teach this lesson to us but we're having a quiz about this tomorrow. Thanks a lot.

@iamthejustin7420 8 лет назад

omg what would happen if khan academy dies, then i would fail every maths test LOVE YOU KHAN ACADEMY KEEP IT UP

@rajatkamalpolisety2864 7 лет назад

khan academy will never die (sal will tho :( ) lol

@shannonfernandes1 7 лет назад

Rajatkamal Polisety I will make sal live 4ever

@benwalker3771 9 лет назад

i dont think i would pass tests without you. cheers mate

@diguiane 4 года назад

Now im done with my modules

@just_magneee3185 3 года назад

Teacher in this academy is better than my teacher.

@stasha8611 3 года назад

That really helped

@valeriecrespo4637 4 года назад

What if you have to solve for no real solutions with [i]

@mikeadriano4391 4 года назад

you can still solve them using the formula. if b^2-4ac is negative [(-b^2+4ac)^(1/2)].i equals to (b^2-4ac)^(1/2)

@TheWhatnow9999 10 лет назад

You save my math life thank you so much

@bryannguyen658 10 лет назад

Agree

@GEGE77R6 9 лет назад

+Bryan Nguyen +Ryan Houston he may have saved your math lives but your grammar lives needs work.

@AliceDiableaux 9 лет назад

+GEGE77R6 How can you possibly deduct anything about someone's mastery of English grammar when he only commented one word?? Jackass

@aletheaplass6557 4 года назад

Your handwriting is superb

@noblessus 14 лет назад

I really like your videos Sal, they are very useful for me. Quick comment: Instead of saying discriminant=zero means one solution, I know it would have saved me many hours of research if someone told me that we still have two solutions (like always with quadratics) but in this case the solution repeats two times. Eg: x^2-4*x+4, even though it's discriminant is zero, it still has two solutions, which are x=2 and x=2. Again great videos and I hope you do more calculus and physics videos!

@YamenNazer 5 лет назад

This is very good i loved it..but i have a question..how did we explore the formula of discriminant ?

@dimeg52 3 года назад

I’m taking algebra 2 this year and the original algebra 2 teacher went to another school and now I’m stuck with a teacher who’s said he has never taught this before. So, this really saving my career.

@ForEvaW15h1nG 13 лет назад

Well... the consistancy in your video's is through the roof. i've just started A levels after getting a good grade in Math in Gcse ... there is quite some confusion among the topics i'm studying in this new curriculum... some of the topics i've had trouble in I've searched for help, YOU have covered them all. Thank you.

@thepostmandelivers.5124 8 лет назад

Great video straight to the point and clear, great job

@sen-te8oq 4 года назад

i can safely say this explained and taught me more than my school.

@monicaairamonserate7471 5 лет назад

omyghad, thankyouuu!!! ❤️

@twominutepenalty 13 лет назад

@Rowan9789 if 5x^2-6x=0 the constant is zero. you could feasibly write the same equation as 5x^2-6x+0=0. either way, the y-intercept would be 0, as would the x-intercept.

@Karin6509 7 лет назад

So I put the "i" at the end of the solution in Aleks when the answer is negative?

@drewneugilos8681 6 лет назад

Is B always negative?

@zingerburgerbox8806 6 лет назад

ItsYour Gamer yes, it’s part of the equation.

@SirNanothy 4 года назад

if the value for B is already negative, then when you plug it into the quadratic formula it would then be positive.

@metallizard88 3 года назад

I actually started jumping of joy because I finally understood it

@TomarAshish 2 года назад

Thank you! ❤️

@crazer96 12 лет назад

It touches the x-axis in two places, so the parabola goes down touches one point on the x-axis and then when it comes up again it touches a different point on the x axis.

@xiaoxiao5088 Год назад

Can we use the discriminant formula when the equation in linear?

@shhzaid 2 года назад

Thank u khan acedmy

@awol9914 8 лет назад

Very helpful. Thanks!

@clairenime Год назад

5:42 wouldn’t you move the a to the other end with everything else? My teacher says x^2 has to be positive

@shizu019 3 года назад

You save me from my sufferring thank you

@Dusevic 14 лет назад

wooooohooo imaginary numbers!!!! u should add imaginary numbers to your linear algebra playlist. 'cause it would help me with my college course! especially rref'ing a system composed of imaginary numbers

@ahmedsarker3555 4 года назад

sir khan one question, for the first discriminant which is bsquare - 4ac > 0 you said there will be two solutions positive and negatice but in this case, the negative is less than zero so how come there can be two solutions. In this case can we say both the values which are executed are positive instead of one postive and one negative since it would consider that one of them is greater than zero but not the other one

@rushikeshsurywanshi2286 4 года назад

Iam watching it now and thanks

@jacobrodriguez9980 10 лет назад

How will I know if it is rational or irrational ?? And how will I know if it is complex ??

@rascaldevilz 12 лет назад

how does two solution look like in graph ??

@nathanaellandicho 8 лет назад

it's gonna form a parabola. the two solutions are the two points where the parabola will hit the x-axis.

@obendesmond 4 года назад

Hello sir, please which software are you using to teach? its pretty cool

@anaisperez2704 3 года назад

i wish i had you as my teacher instead sal

@sebru 3 года назад

is there a nature of roots video? i cant find one and this is the lesson in my school

@user-tu6hq8hu1r 2 года назад

Thanks

@iiiijoseuy 8 лет назад

what real life application does using the discriminant have?

@HPatel-vf7ih 7 лет назад

You can use it for engineering (and stuff like that). Also, if you want to go to law school or med school you have to know it.

@HPatel-vf7ih 7 лет назад

SpiritWolf2K Hahahahha, yeah.

@kamilo1175 6 лет назад

oJose developing your brain

@shreyanshpandey4022 6 лет назад

Employment 😂😂😂😂

@uttkarshjha8265 3 года назад

My god 11 years ago Cant belive

@paulceltics 13 лет назад

@loversjustkeeploven really? thats pretty awesome

@GndmMkv 14 лет назад

man it helped so much that i feel like not going to school anymore

@elbay2 14 лет назад

Well done! What S/W and H/W set-up do you use as a "black board"? It's very easy on the eyes!

@theophonchana5025 2 года назад

x^(2) + 3x - 6 = 0 x = (-3 + sqrt (-15)) ÷ 2 x = error

@yellowblob3573 7 лет назад

THANK YOU SOOOOO MUCH (:

@moonmoonmoon11 10 лет назад

how did u get 4?!!!!

@dylangarcia7314 3 года назад

if the discriminant b^2-4ac=0, the graph of f(x)=ax^2+bx+c, a not equal to 0, will touch the x-axis at its vertex? True or false?

@theophonchana5025 2 года назад

b^(2) - 4ac = -15

@ayyoitzToko 11 лет назад

aiight bro. cya

@randhawaheed2720 5 лет назад

THANK YOU THIS IS SO GOOD but I've a question how does it matter if it is a rational solution or an irrational solution

@KayMarie-es3cr 5 лет назад

Nobody Iknow Yes.

@randhawaheed2720 5 лет назад

@@KayMarie-es3cr what does yes mean

@KayMarie-es3cr 5 лет назад

Nobody Iknow Sorry. I thought you asked if it matters if it’s rational or not

@randhawaheed2720 5 лет назад

@@KayMarie-es3cr it is completely fine but do you know how it matters if so

@KayMarie-es3cr 5 лет назад

Nobody Iknow do you mean why it matters?

@kannanr837 7 лет назад

@khan how come we get 2 parabola for a quadratic equation... won't the graph be a single parabola that meets x-axis twice...

@Ice_Screamer 7 месяцев назад

helpful af

@girlicious102 14 лет назад

thankss this video helped alot

@shannonfernandes1 7 лет назад

gucci jessi hey

@빨갱유모차길냥맘 5 лет назад

판별식이 0이라는것은 곧 2차방정식이 완전제곱식의 형태라는 것과 같네요 잘 배우고 갑니다

@jamieg6173 8 лет назад

SO HELPFUL! Thank you!

@universalponcho 2 года назад

This is dope

@pitrochied 3 года назад

watching after 11 years also.....

@noobkosh 12 лет назад

why I cant find this video in the website??

@gkgames7589 4 года назад

what if its not equal to 0 and hahs 4 numbers in the equation

@loversjustkeeploven 13 лет назад

@paulceltics yea seriously. i live alone but my parents still support me. and they would have made me enlist of i didnt end the my junior year with C's.

@xcelpast 13 лет назад

thanks bro

@peterpro9250 2 года назад

What if the real solution isn't rational??? Pls tell

@akeelahmad821 6 лет назад

If there is cubic equation?

@marlyjoysereno1264 7 лет назад

wait,wait so where do you get on 5:24 (the orange color) there is discriminant so where did you get the 9-4? ( Discriminant 9-4(1)(6) )

@sun0tea 7 лет назад

b is 3 so b squared is 9. You subtract 4ac from b. 4*a (which is1)*c(which is 6) So, b-4ac is 9-4*1*6

@omardotbio 6 лет назад

a must be equal to -1 not 1

@moonmoonmoon11 10 лет назад

oh never mind!!!!!! :)

@hongrand 9 лет назад

Thank you!

@user-uwo 6 лет назад

thank you for the arabic translation

@shobharanipl6129 6 лет назад

amazing

@haideralikhan5976 3 года назад

love ya mate, noice

@jyavant 8 лет назад

What about for all real numbers?

@labeebahmad6287 4 года назад

Khan academy should be the most subscribed channel on RU-vid change my mind

@wardairfan9074 6 лет назад

Can anyone give me an example of discriminant

@Chaosflyex98 12 лет назад

You are way better than my math teacher, and I wish you were my science teacher because he is just so... argh. =__=

@abdias99 3 года назад

I learned more in 10 mins than in 2 hours from my class thx 🙏🏽

@looking_33 8 лет назад

Why am I learning this in algebra 1 if this is algebra 2

@handler514 4 года назад

lookinglasstie did u find your answer after 3 years?

@0illuminate 4 года назад

0 illuminate

@Chaosflyex98 11 лет назад

I don't have a point. My comment had nothing to with you. Now good day, sir.

@Chaosflyex98 11 лет назад

I'm quite surprised that you replied to me after 11 months. Smh..

@HACKER-BHAVESH 3 года назад

Omg 10 year ago

@ImFlamez 6 лет назад

With the internet, who needs school?

@foxenbox 3 года назад

I miss 2010

@YBNKASHWAYS 3 года назад

Same

@IcedLipGloss 12 лет назад

IF ONLY MY MATH TEACHER TAUGHT LIKE THIS -____-

@fabiogaming9268 6 лет назад

JOE LIKES GUYS

@joejones7936 11 лет назад

The discriminant of the 3rd equation is 9489.000000000002

@hansanderson8599 7 лет назад

the third example is not a perfect square, it is 7567 and the square root of that is 86.98850499...

@HPatel-vf7ih 7 лет назад

There are other square roots that might go into that number. (4,9,16,25,36,49,64,81 etc.)

@ayyoitzToko 11 лет назад

it's what BRO? huh whats wrong with saying BRO

@shannonfernandes1 7 лет назад

J UnknWn lets see after 4 years

@abigailmiller7193 6 лет назад

How about 5 years

@millianford7389 5 лет назад

How about 6 years

@benhawk4214 5 лет назад

@@millianford7389 6 years and one month

@skuffd-semicolon 5 лет назад

@@benhawk4214 6 years and 5 months anyone? Also, a little time capsule for you 202x peeps: the year is 2019. Memes still exist and currently we are facing the death of "say sike right now" and the meme community is well saturated with Pewdiepie slang such as "bing bong". Speaking of Pewdiepie, last week he hit 100 mil subscribers, got married to Marzia, and killed the ender dragon in his very popular Minecraft series.