Having seen a few videos from khan academy, worked with various math websites, even tried a book algebra 1 for dummies, this is MILES ahead of everything else. The way you get to the point and pack everything densely, yet still manage to explain everything fully is amazing. This entire polynomials only took me a good hour to master. Thanks!
I did the same of my god khan academy was a pain in algebra I did pre-algebra was getting trough algebra but I waas feling that I wasn't learning. And finnaly I decided to try RUclips and by chance found this channel sent from heaven.
Ya same here brother, still chipping away at the series? How far have you made it and how is your comprehension? I've been practicing my math on Khan Academy while re-learning from this channel.
As a G11 STEM student studying math for my college entrance exam, I thank you Math Jesus from the very bottom of my heart for this playlist. This makes math so easy to understand. Love from the Philippines 🇵🇭 🫶🏻
Thank you for this! I seriously never learned to derive the quadratic formula in HS. I always just did it. But now I LOVE knowing the whys of math. Thank you!!
I think an important point that should be emphasized in explaining the derivation of the quadratic formula is making sure people don't confuse coefficients with variables; they shouldn't treat the coefficients a,b, and c in the same manner they treat the variable x. It is so easy to see a letter in algebra and automatically treat it as a variable even in situations where the letter stands as a coefficient for a constant. This was a big stumbling block for me when I was first taught how to derive this formula. I suspect many people who learn this will have a similar struggle.
when you are in a real expression, you don't have the coefficients written as variable, you have only numbers, so every letter is an unkown you must find. Only in examples you have coefficients written as letters, but if you notice coefficients are letter at the beggining of the alphabet, as a b c etc..., and unkowns at the end of the alphabet, as x y z.
I've never been this pissed bro my teacher briefed through this formula like a side hustle when infact I could've solved polynomials in 3 secs with this....literally dropped it last 15 secs of class and told us to remember w/o telling anyone it's purpose
Wow, honestly a crazy good series! Poignant explanations, no getting caught up in unnecessarily complicated academic terminology, structured perfectly logically from episode to episode. Makes all of this seem super easy - which it is with the right teacher! Really helping me brush up on my fundamentals. Thanks so much!
On the 2nd question here in 6:10 why are both the answers positive? -13 + 11 over 6 is -1 over 3 (simplest form) -13 -11 over 6 is -4 since the answer is -24 over 6 Can someone explain pls
It 13 not -13 because b is the real number(positive or negative)that being multiplied by x that we apply the quadratic formula in that equation -b is -(-3) which is 3 hope i did answer you question
@@Stoirelius They are needed between the numbers in the actual calculation (4*8 and 2*8) so I also put them in the Quadratic Formula at the top to make it easier to reference from one to the other. But you're right, the Quadratic Formula could be written x = (-b ± √(b^2 - 4ac)) / 2a
Thanks, Dave! In school I remember all they told us was the formula itself and that if we plug in the numbers and do the arithmetic right we'll get the answer. But until seeing this video I had never actually seen an explanation of what the formula actually is or the logic behind it! Teaching the actual subject, what a novel idea!
I can still remember the quadratic equation 35 years after learning it. This video is a good refresher on what it actually means as 10 minutes ago I didn't have a clue.
2 squared is 4, then do 4*1*-3 left to right, giving -12. Then you have 4- -12 effectively giving 4 + 12 = 16. It was ugly and took me a while too. It helped me to refer back to the original formula and do it mentally rather than look at all those parentheses with the a,b,c terms plugged in.
when subtracting or adding fractions, each fraction should have the same denominator. so to get the c/a to have the same denominator as b^2/4a^2, you multiply 4a/4a to c/a.
Wow, something messed up when my reply printed. Let's try it again. The b value is minus 13, so when it is plugged into the formula, the minus 13 is minus minus 13, or just 13.
First do the parenthesis, so u can do -4 x 1 to get -4 and then multiply that with -3 to get positive twelve, since when there are no symbols multiplication is assumed. (For example (2)(3) would be 2x3 which is 6.) So since we got -4 with -4(1) and then multiplied that by -3 to get POSITIVE twelve now its 2^2 + 12, the addition symbol coming from the fact the twelve is now positive. Basically, follow PEMDAS.
I don't understand. He said at 0:40 that sometimes, the "completing the square" method won't work ("neither of these strategies will work"), so that's why he introduced the 3rd method, the quadratic formula. But the quadratic formula IS the completing the square method! How can one thing work and the other not if they are the same thing? I've tested the completing the square method for all the examples given here and it works.
Can you tell me when he actually said they wouldn't work? I checked the part you mentioned and found that he had said, "neither of these will be easy or possible to perform" that simply means they can be done but for us normal humans, it can be almost impossible to do; even though they can be used to solve, we might not be able to do so.
@@Tusharplays69 Technically, completing the square can always work, it just involves fractional terms. There are cases where you cannot solve quadratics with real solutions, but solving a quadratic in general is still always possible, when you extend your solution set to all complex numbers.
It doesn't really make sense to me to treat a, b, and c as constants, because we try to build a formula that will accept different values, so if treating them like variables, meaning that √4a^2 = ±2a, it should be alright because we already have a ± in the expression that deals with every possibility. I'm not sure though :|
Bro this whole time during HS I was forcing myself to learn the quadratic formula. I never knew how we figure out the formula. But now it’s unbelievable. It all makes sense 😭 Thank you professor Dave
One example of where you would use a quadratic formula in physics, is solving conservation of momentum, and conservation of kinetic energy, as you do in collision analysis.
Hi, professional Dave thank you so much for making these amazing videos. COMPREHENSION 1 SOLUTION: -(5) ±√(5)² - 4(2)(-25) x = ------------------------------- 2(2) -(5) ±√225 x = ----------------- 2(2) -(5) + 15 x = ----------- 2(2) -(5) + 15 x = --------- 4 -(5) - 15 x = ---------- 4 2 real solution ? "I'm not sure" 10 x = ------ 4 -20 x = ----- 4
So the quadratic formula is completing the square but it skips to the last step. Great for squares that will involve complicated fractions but cumbersome for simpler equations.
Babylonians already knew how to solve quadratic equations - their solution just had a different form because their initial equation had a different form. Obviously its not difficult if the solution is 4000 years old. And if you want to be pedantic then sridharacharya didn't give the complete solution either en.wikipedia.org/wiki/Babylonian_mathematics#Algebra en.wikipedia.org/wiki/Quadratic_equation#History
Just like pascal triangle It also has many name like Yanghui triangle and Suno triangle Actually some formula already known in vet long time before someone discovered it Name is just for us easy to know it So the most important is just we must understanding theory of background regardless to argue about the name If you want to use that name for that formula it is depand on you
Having seen a few videos from khan academy, worked with various math websites, even tried a book algebra 1 for dummies, this is MILES ahead of everything else. The way you get to the point and pack everything densely, yet still manage to explain everything fully is amazing. This entire polynomials only took me a good hour to master. Thanks!
I did the same of my god khan academy was a pain in algebra I did pre-algebra was getting trough algebra but I waas feling that I wasn't learning. And finnaly I decided to try RUclips and by chance found this channel sent from heaven.
What a god of maths, watching these videos and it's changing how I see maths
Ya same here brother, still chipping away at the series? How far have you made it and how is your comprehension? I've been practicing my math on Khan Academy while re-learning from this channel.
As a G11 STEM student studying math for my college entrance exam, I thank you Math Jesus from the very bottom of my heart for this playlist. This makes math so easy to understand. Love from the Philippines 🇵🇭 🫶🏻
Thank you for this! I seriously never learned to derive the quadratic formula in HS. I always just did it. But now I LOVE knowing the whys of math. Thank you!!
But I am happy that I am watching this on HS. Maybe I am lucky that proffessor Dave is in my HS period
I think an important point that should be emphasized in explaining the derivation of the quadratic formula is making sure people don't confuse coefficients with variables; they shouldn't treat the coefficients a,b, and c in the same manner they treat the variable x. It is so easy to see a letter in algebra and automatically treat it as a variable even in situations where the letter stands as a coefficient for a constant. This was a big stumbling block for me when I was first taught how to derive this formula. I suspect many people who learn this will have a similar struggle.
when you are in a real expression, you don't have the coefficients written as variable, you have only numbers, so every letter is an unkown you must find. Only in examples you have coefficients written as letters, but if you notice coefficients are letter at the beggining of the alphabet, as a b c etc..., and unkowns at the end of the alphabet, as x y z.
The real taste of mathematics comes over here when you not just lethal yourself from the formulas else by learning the real concepts.
Thanks Sir Dave
I've never been this pissed bro my teacher briefed through this formula like a side hustle when infact I could've solved polynomials in 3 secs with this....literally dropped it last 15 secs of class and told us to remember w/o telling anyone it's purpose
Wow, honestly a crazy good series! Poignant explanations, no getting caught up in unnecessarily complicated academic terminology, structured perfectly logically from episode to episode. Makes all of this seem super easy - which it is with the right teacher! Really helping me brush up on my fundamentals. Thanks so much!
On the 2nd question here in 6:10 why are both the answers positive?
-13 + 11 over 6 is -1 over 3 (simplest form)
-13 -11 over 6 is -4 since the answer is -24 over 6
Can someone explain pls
It 13 not -13 because b is the real number(positive or negative)that being multiplied by x that we apply the quadratic formula in that equation -b is -(-3) which is 3 hope i did answer you question
COMPREHENSION #3 SOLUTION
Quadratic Polynomial form: ax^2 + bx - c = 0
Quadratic Formula: x = (-b ± √(b^2 - 4*a*c)) / (2*a) - Lots of extra brackets to make precedence clear because I'm only writing on one line.
8x^2 + 14x - 15 = 0
∴ x = (-14 ± √(14^2 - 4*8*(-15)) / (2*8)
∴ x = (-14 ± √(196 - (-480)) / 16
∴ x = (-14 ± √(196 + 480)) / 16
∴ x = (-14 ± √676) / 16
∴ x = (-14 ± 26) / 16
∴ x = 12/16 or -40/16
∴ x = 3/4 or -5/2
i swear to god if i make ONE MORE SIGN ERROR I WILL JUMP OFF A BRIDGE
You don't need to add asterisks.
@@Stoirelius They are needed between the numbers in the actual calculation (4*8 and 2*8) so I also put them in the Quadratic Formula at the top to make it easier to reference from one to the other. But you're right, the Quadratic Formula could be written x = (-b ± √(b^2 - 4ac)) / 2a
nick. you left us 1 year ago, but you still keep saving my life with these comments, i'm so grateful you exist. very very grateful.
THANK YOU NICK you won't be forgotten
Thanks, Dave! In school I remember all they told us was the formula itself and that if we plug in the numbers and do the arithmetic right we'll get the answer. But until seeing this video I had never actually seen an explanation of what the formula actually is or the logic behind it! Teaching the actual subject, what a novel idea!
I can still remember the quadratic equation 35 years after learning it. This video is a good refresher on what it actually means as 10 minutes ago I didn't have a clue.
Game changer 😍😍😍
NEVER BACK DOWN NEVER WHAT⁉️⁉️
NEVER GIVE UP,‼️💯🙏😭
I actually crying, I'm not lying. I am crying because i was so lazy human that doesn't want to learn math before😂
@@Carrymejane The first days of learning are usually the hardest
First time feeling math is beautiful... at 22... starting physics major... wish me luck
it just blew my mind - in a good sense ❤
Underrated videos...
Sir... E=mc^2 plsss
dude, i did one on that already! check out my four-part series on special relativity in the modern physics playlist.
Professor Dave Explains NO WAY. I'm binge watching that now
Thanks Professor! You're such a great person to give such beautiful FREE lessons on RUclips! Unbelievable.
how did you combine it in 4:31 pls help
2 squared is 4, then do 4*1*-3 left to right, giving -12. Then you have 4- -12 effectively giving 4 + 12 = 16.
It was ugly and took me a while too. It helped me to refer back to the original formula and do it mentally rather than look at all those parentheses with the a,b,c terms plugged in.
@@JackMessenger-p1h thanks champ
2:32 question, where did the 4a/4a come from?
when subtracting or adding fractions, each fraction should have the same denominator. so to get the c/a to have the same denominator as b^2/4a^2, you multiply 4a/4a to c/a.
4a/4a equals 1 so multipling by one wont change anything so allowed to your allowed to do this
incredible! wow, very good teaching method. thank you professor dave!
for item #2, are the answers (+)'s or (--)'s?. coz im getting (-4 & -1/3). thanks!
The "b" value is -13, so when it is plugged into the formula, the "-b" is "- -13" or just 13. It's an easy thing to miss.
Wow, something messed up when my reply printed. Let's try it again. The b value is minus 13, so when it is plugged into the formula, the minus 13 is minus minus 13, or just 13.
So is it ok to not know {factoring method} and {completing square method}..
If you know how to solve using quadratic formula?
I skipped previous two videos....
Pretty much, yes.
at minute 4:33, how did he get 16? I got -8. Can someone help please
Same, help dave
Help me too
First do the parenthesis, so u can do -4 x 1 to get -4 and then multiply that with -3 to get positive twelve, since when there are no symbols multiplication is assumed. (For example (2)(3) would be 2x3 which is 6.) So since we got -4 with -4(1) and then multiplied that by -3 to get POSITIVE twelve now its 2^2 + 12, the addition symbol coming from the fact the twelve is now positive. Basically, follow PEMDAS.
I don't understand. He said at 0:40 that sometimes, the "completing the square" method won't work ("neither of these strategies will work"), so that's why he introduced the 3rd method, the quadratic formula. But the quadratic formula IS the completing the square method! How can one thing work and the other not if they are the same thing? I've tested the completing the square method for all the examples given here and it works.
Can you tell me when he actually said they wouldn't work? I checked the part you mentioned and found that he had said, "neither of these will be easy or possible to perform" that simply means they can be done but for us normal humans, it can be almost impossible to do; even though they can be used to solve, we might not be able to do so.
@@Tusharplays69 Technically, completing the square can always work, it just involves fractional terms.
There are cases where you cannot solve quadratics with real solutions, but solving a quadratic in general is still always possible, when you extend your solution set to all complex numbers.
3:02 How did we come up to that solution where square root of '4a*square' is pure '2a'. Where is '-2a' ?!
It doesn't really make sense to me to treat a, b, and c as constants, because we try to build a formula that will accept different values, so if treating them like variables, meaning that √4a^2 = ±2a, it should be alright because we already have a ± in the expression that deals with every possibility.
I'm not sure though :|
Bro this whole time during HS I was forcing myself to learn the quadratic formula. I never knew how we figure out the formula. But now it’s unbelievable. It all makes sense 😭
Thank you professor Dave
I just know this one i use this every time and mastered it so it became more easy to me than other easier methods 😂
In India, this formula is known as shri dharacharaya rule
@Allan 112358 Right
Woah it takes me 3 days to comeback here again after learning total about polynomials
ty
Thanks allot Dave❤️
Great! We got a first serious formula on our hands. I will celebrate this with a cake with 1/∞ candles on it.
Whoever invented this formula should be praised for eternity.
It was sridharacharya
Function and relation please...sir
So if I already know the quadratic formula, do I still have to remember how to complete a square and how to factor
6:19 How come it's 1/3 can anyone explained it to me? 😅
Given:
3*x^2 - 13*x + 4 = 0
The coefficients are as follows:
a = 3, b = -13, c = 4
Plug in to the quadratic formula:
x = (-b +/-sqrt(b^2 - 4*a*c))/(2*a)
x = (-(-13) +/-sqrt(13^2 - 4*3*4))/(2*3)
x = (13 +/-sqrt(121))/6
x = (13 +/- 11)/6
Upper root
x2 = (13 + 11)/6 = 24/6 = 4
Lower root:
x1 = (13 - 11)/6 = 2/6 = 1/3
Trigonometry plzzz
patience, that's coming!
are quadratic equation nescessary for learning physics.
yes, and much more advanced math than that
yes.
One example of where you would use a quadratic formula in physics, is solving conservation of momentum, and conservation of kinetic energy, as you do in collision analysis.
How did you guys solve the 3rd comprehension?
Shree dhara charaya invented this formula
the quadratic formula is not the invention of a single person but rather the result of mathematical development across cultures.
Hi, professional Dave thank you so much for making these amazing videos.
COMPREHENSION 1 SOLUTION:
-(5) ±√(5)² - 4(2)(-25)
x = -------------------------------
2(2)
-(5) ±√225
x = -----------------
2(2)
-(5) + 15
x = -----------
2(2)
-(5) + 15
x = ---------
4
-(5) - 15
x = ----------
4
2 real solution ? "I'm not sure"
10
x = ------
4
-20
x = -----
4
So the quadratic formula is completing the square but it skips to the last step. Great for squares that will involve complicated fractions but cumbersome for simpler equations.
Is anyone else not getting anything close to the actual answers for comprehension problems?
Ok I figured out what I was doing wrong; I was doing subtraction at the step where b^2 - 4ac instead of "combining"
How can it be expressed by (x-1)(x+3)=0
Watch his video, 'Solving Quadratics by Factoring' and you'll understand why.
Last tune is like mario tune I like it
For 3rd the signs are opposite of the answers shown in the video i.e. -3/4, 5/2
the solution is correct you should check/double check your + and - signs
(-c/a*4a/4a=-4ac/4a^2) why only one side
❤❤❤
Done.
Isn't that formula only for =0 ?
I wish I watched that in 11th grade
please cut your hair!!! love the vids.! thank you!
This video is 5 yrs old... and he did, not that it matter anyway.
@@carl8790 yeah, that’s true
Nothing hits like the feeling of finally getting a math problem
sridhcharya formula
I prefer fhe completing square much ez
Sir this formula was given by Indian mathematician "Sridharachrya"
Please use his name.
lol no. This formula was known by ancient Babylonians 2500 years before he was even born.
en.m.wikipedia.org/wiki/Sridhara
Wikipedia clearly written that this formula firstly used by sridharacharya
Babylonians already knew how to solve quadratic equations - their solution just had a different form because their initial equation had a different form. Obviously its not difficult if the solution is 4000 years old. And if you want to be pedantic then sridharacharya didn't give the complete solution either
en.wikipedia.org/wiki/Babylonian_mathematics#Algebra
en.wikipedia.org/wiki/Quadratic_equation#History
Just like pascal triangle
It also has many name like Yanghui triangle and Suno triangle
Actually some formula already known in vet long time before someone discovered it
Name is just for us easy to know it
So the most important is just we must understanding theory of background regardless to argue about the name
If you want to use that name for that formula it is depand on you