That tik tak toe factoring method was awesome. I've never seen that before, but it is a much neater way than the AC method I've been using. I love this channel, always learning something new. And even if it is something I already know, I seem to discover new insights and nuances to those concepts. Nice work man. Keep these awesome videos coming! Clearly though, I need to get a life, I'm having way too much fun watching math videos on a Friday night. I'm such a nerd.
in my view there are only 3 ways: 1) factoring (if the problem allows for it) 2) quad formula 3) completing the square and then square rooting both sides. the method of just square rooting both sides only works if they already give you something with a complete square. in other words, it is the wrapping up of method 3. it's kind of like if they give you something that's already factored. just use the zero product property, but that's wrapping up method 1. from the form ax^2+bx+c=0, there is no way to just take square roots. you need to use one of the 3 methods above.
(Best) Method 5: (derivative)^2 = discriminant. So, ax^2 + bx + c = 0 becomes (2ax+b)^2 = b^2-4ac. Rest is easy to solve by taking square root on both sides. The origin of this method is from ancient Indian Vedic mathematics (the original formula was in Sanskrit - चलित कलित वर्गो विवेचकः )
seriously, thank you for making these videos!! all of them help me a lot, and you explain it all in-depth and perfectly. I'm sure many other people including me appreciated your daily uploads~ keep it up!
I always use the normal form formula, i.e. bring the equation into the form x²+ p x + q = 0. Then the result is x = - p/2 +- sqrt(p²/4 - q). If the equation is already of the form ax² + bx + c = 0, then just divide it all by a to get the normal form.
"M plus or minus square root of m squared minus p." (3blue1brown/Acapella Science) M = -b/2, P = [not to be confused with your linear variable] c, because b is the negative sum of the roots and c is their product.
I know another way to solve quadratic It works also for cubics and quartics First lets create system of equation x_{1}-x_{2}=d x_{1}+x_{2}=-a_{1} Last equation is sum of the roots and from Vieta we know that it is equal -\frac{a_{1}}{a_{2}} and I assumed that a_{2}=1 Discriminant is symmetric function of the roots and we can transform first equation to be a discriminant x_{1}-x_{2}=d x_{1}+x_{2}=-a_{1} (x_{1}-x_{2})^2=d^2 x_{1}+x_{2}=-a_{1} (x_{1}+x_{2})^2-4x_{1}x_{2}=d^2 x_{1}+x_{2}=-a_{1} a_{1}^2-4a_{0}=d^2 x_{1}+x_{2}=-a_{1} 2x_{1}=-a_{1}+d 2x_{2}=-a_{1}-d For cubics and quartics you have to create resolvent equation instead of using discriminant
I have another method for the first one : (3x-5)*(x+2)=4*5 (3x-10)*(x+2)=(3*3-5)*(3+2) then x=3 is a first solution by identification and according to the polynomial formula : a(x-3)(x-b)=0 thus a=3 and b*a*(-3) should equal (-30) because -30 is our constant in this equation so 3(x-3)(x+10\3)=0 and ×=-10\3 is a 2nd sol.
The Quadtratic Formula is so important in german maths education, that it's called the "Mitternachtsformel" which means "midnight formula". It's called that, because if someone wakes you up in the middle of the night and asks you what the formula is, you sould know it by heart.
Here is a fifth way, guessing. The RHS is 20 which factors to 5*4 By inspection x=3 gives (9-5)*(3+2) =20 Can’t find the second root by inspection, so find the stationary point by differentiation Of the x x^2 terms Which is the average of the roots (3X^x +x)' = 6x+1 =0 , Xm=-1/6. =(xr +3)/2 xr =-10/3
Is it too advanced to explain the benefits of being able to solve by complete the square? I wish I knew earlier how much it would help when it comes to graphing polynomials. This can even help in calculus with curve sketching sometimes because you need not always take the derivative then find its zeroes, etc if you already can get the graph of the polynomial by doing some function transformations that can be found by completing the square. A polynomial in '(x + p)^2 + c' form is great for graphing for the p & c tell you how much of a shift you need to do to the x^2 polynomial to get the one you want to graph. No derivative & zeroes needed.
I think I know what you mean: normalize by dividing by a, then write as x^2 - sx + p (s= sum, p= product) The solutions are (s = -2m ) m+/- sqrt (m^2 - p) which is exactly the same as the regular quadratic formula. (3Blue1Brown and Acapella Science described this method in a video on eigenvalues)
Nicolas Heringer that's just a small milestone. I do have videos with over 50000 views but I want to have this video being the first algebra video to be over 10000 views. : )
So basically I need to know at least two different methods(or should I learn all of them..I hate using too many methods for one thing)....one when factorable and one when factoring is not an option? I saw you did some stuff to rearrange the order of the equation....transfer the equal sign from left to right....what is that???! And you also reformed the first problem (looked like what you get after factoring a trinomial) into a normal looking quadratic equation!?!? I understand a quad equation can be factorable or not,but what is it with all the varying appearances?...it's annoying to me...3x^2+ -8- 12=0..........................(3x+5)(2x+5)..........3x^2=6x+9........how many variations are there and why
@blackpenredpen it's been a year but the views have reached 10k are we getting the song?
He has to sing it 3 times by now
@@Л.С.Мото 5 times now
@@tejasdeepsingh456 6 times
@@Л.С.Мото 7 times
@@Л.С.Мото 8 times
4 ways to solve quadratic equations
blackpenredpen 只能說配方法萬能了
Azir The Emperor of the Sands 是的！
Pdf dont work
When will you sing the quadratic formula song? Look at the view count 現在(12/6/2018)觀看次數：13,955
啦！ 曹老師請你快唱《二次方程之歌》吧！
I have the fifth way k
That tik tak toe factoring method was awesome. I've never seen that before, but it is a much neater way than the AC method I've been using. I love this channel, always learning something new. And even if it is something I already know, I seem to discover new insights and nuances to those concepts. Nice work man. Keep these awesome videos coming! Clearly though, I need to get a life, I'm having way too much fun watching math videos on a Friday night. I'm such a nerd.
I’m more of a Slide and Divide person, but Tic-Tac-Toe does look more fun.
in my view there are only 3 ways:
1) factoring (if the problem allows for it)
2) quad formula
3) completing the square and then square rooting both sides.
the method of just square rooting both sides only works if they already give you something with a complete square. in other words, it is the wrapping up of method 3. it's kind of like if they give you something that's already factored. just use the zero product property, but that's wrapping up method 1.
from the form ax^2+bx+c=0, there is no way to just take square roots. you need to use one of the 3 methods above.
Right
Taking the square root is useful when given vertex form though
Great video... Did you sing the quadratic formula song? :0
(Best) Method 5: (derivative)^2 = discriminant. So, ax^2 + bx + c = 0 becomes (2ax+b)^2 = b^2-4ac. Rest is easy to solve by taking square root on both sides. The origin of this method is from ancient Indian Vedic mathematics (the original formula was in Sanskrit - चलित कलित वर्गो विवेचकः )
isn't this basically just the quadratic formula, if you square root both sides, then do -b and divide by 2a?
@@geryz7549 yeah i agree this is just quadratic formula but with more steps
seriously, thank you for making these videos!! all of them help me a lot, and you explain it all in-depth and perfectly. I'm sure many other people including me appreciated your daily uploads~ keep it up!
ashleigh 2.0 thank you for your nice words and I will
i already knew the quadratic formula. but lets just make him sing!
I m down lol
I love you... just kidding. That’s gay. - but you are helpful.
@@blackpenredpen sing now.
I hope this helps me with my GED
I take it in 2 days!
thanks for the video
I've never heard the Quadratic Equation Song. I'm anxious to hear it now.... even if I have to review algebra to get it.
Well done. Very well done 👏🏿👏🏿👏🏿
Good role model for us
A good teacher has to keep his promise. When do we hear you sing the quadratic formula song?
True- he's gotten over 80K views!
I always use the normal form formula, i.e. bring the equation into the form x²+ p x + q = 0. Then the result is x = - p/2 +- sqrt(p²/4 - q).
If the equation is already of the form ax² + bx + c = 0, then just divide it all by a to get the normal form.
"M plus or minus square root of m squared minus p." (3blue1brown/Acapella Science) M = -b/2, P = [not to be confused with your linear variable] c, because b is the negative sum of the roots and c is their product.
Almost 8000 views. You need to promote this video
THANK YOU SO MUCH OUR TEACHER DOESNT EVEN TEACH AND THIS TAUGHT ME SO MUCH
excuse me but couldn’t we use the formula of the special trinomial at point 1:46?
what an awesome dude, I started using a black pen and red pen(and pencil) and I always think of him :)
Break it down my bother!!!! Great job..
Thank yoooooouuuuuuuuuuuuu! you are the best sz
You seem so nice! Thank you so much for this video :3
Excellent leasson teacher
Just exemple ( 3x - 1 ) (2× - 1 )= 0
Thank you teacher
See you
I know another way to solve quadratic
It works also for cubics and quartics
First lets create system of equation
x_{1}-x_{2}=d
x_{1}+x_{2}=-a_{1}
Last equation is sum of the roots and from Vieta we know that it is equal -\frac{a_{1}}{a_{2}}
and I assumed that a_{2}=1
Discriminant is symmetric function of the roots and we can transform first equation to be a discriminant
x_{1}-x_{2}=d
x_{1}+x_{2}=-a_{1}
(x_{1}-x_{2})^2=d^2
x_{1}+x_{2}=-a_{1}
(x_{1}+x_{2})^2-4x_{1}x_{2}=d^2
x_{1}+x_{2}=-a_{1}
a_{1}^2-4a_{0}=d^2
x_{1}+x_{2}=-a_{1}
2x_{1}=-a_{1}+d
2x_{2}=-a_{1}-d
For cubics and quartics you have to create resolvent equation instead of using discriminant
Very well-explained
PDF link not working,..
I have another method for the first one :
(3x-5)*(x+2)=4*5
(3x-10)*(x+2)=(3*3-5)*(3+2)
then x=3 is a first solution by identification and according to the polynomial formula : a(x-3)(x-b)=0
thus a=3 and b*a*(-3) should equal (-30) because -30 is our constant in this equation
so 3(x-3)(x+10\3)=0 and ×=-10\3 is a 2nd sol.
The Link to the pdf is not up anymore
Well you can solve this with differential calculus, give limits to the square (with the help of the deveriate) and use newton's method
Completing the square method can be also used to reduce quartic equation to cubic equation
Love it from india
i always just use the quad formula whenever i see quad equations :D
Thanks for this wonderful video!;)
: ))))
The Quadtratic Formula is so important in german maths education, that it's called the "Mitternachtsformel" which means "midnight formula". It's called that, because if someone wakes you up in the middle of the night and asks you what the formula is, you sould know it by heart.
In der Schule habe ich nie davon gehört, stattdessen haben wir die p-q-Formel benutzt.
@@j0j083 p q Formel ist ja auch ein Müll, welchen man nur im deutschen Müllsystem lernt.
Really you are great.
Where is the pdf file, "page not found" error displayed???
Here is a fifth way, guessing.
The RHS is 20 which factors to 5*4
By inspection x=3 gives (9-5)*(3+2) =20
Can’t find the second root by inspection, so find the stationary point by differentiation Of the x x^2 terms
Which is the average of the roots
(3X^x +x)' = 6x+1 =0 , Xm=-1/6. =(xr +3)/2
xr =-10/3
you are so good
Fifth way : put ( d( ax^2+bx+c)/dx )^2= b^(2) --4ac this gives x1 , x2 directly . Wow !! Dr . Rahul
Is it too advanced to explain the benefits of being able to solve by complete the square? I wish I knew earlier how much it would help when it comes to graphing polynomials. This can even help in calculus with curve sketching sometimes because you need not always take the derivative then find its zeroes, etc if you already can get the graph of the polynomial by doing some function transformations that can be found by completing the square. A polynomial in '(x + p)^2 + c' form is great for graphing for the p & c tell you how much of a shift you need to do to the x^2 polynomial to get the one you want to graph. No derivative & zeroes needed.
We can solve it also by graphing to find the two points of x- intercipt
pdf not found :(
I love the Quadratic formula superiority.
But it was bit harder to do everything mentally.
Pls can you tell me what are the solution of 9t²-6t-8=0 im confused pls tell me the answer and the solution
Remember the quadratic formula :
ax² + bx + c = 0
x = -b ± sqrt(b² - 4ac) / 2a
9t² - 6t - 8 = 0 :
Know that : a = 9,b = -6,c = -8
t = -(-6) ± sqrt((-6)² - 4 (9) (-8)) / 2(9)
=> t = 6 ± sqrt(36 - (-288)) / 18
=> t = 6 ± sqrt(324) / 18
=> t = 6 ± 18 / 18
Therefore,we have other 2 same sol.
t = -⅔ or t = 4/3
I can't find the pdf ?!
I don't really get the right side of the equation to equal 0.
I do: x ² + cx = k → x = (± √ ( 4k + c ² ) - c )/ 2
(3x - 5) (x + 2) = 20
3x^(2) + x - 10 = 20
3x^(2) + x - 30 = 0
(3x + 10) (x - 3) = 0
#trinomial #binomial #polynomial
Thanks. Your links are not working any more... are you still doing this? can you send me a working link? Thank you
what does the i mean in the square roots?
Imaginary number .. i = sqrt(-1)
Nice
Wow, amazing! Made my life so much easier! I'm in love thank you so much! :D
b^(2) - 4ac = 24
10000 here we come!!
Eashaan Singh Lol. Thank you.
@blackpenredpen......as of Dec 26, 2020 there are 64000 views....but no song.....what a bummer!!😑😑😒😒
Bprp you have 10000 views on this video
lol imma share this with my math teacher and get you those 10000 views
Max Bingham lol. Thank you.
I use completing the square in 4th ways and i get x= 1/5 ± √5/5
halfway there before your song
I also know an another method💐🙏
a = 5
b = -2
c = -1
I have another way
Using sum and product of roots
I think I know what you mean: normalize by dividing by a, then write as x^2 - sx + p (s= sum, p= product) The solutions are (s = -2m ) m+/- sqrt (m^2 - p) which is exactly the same as the regular quadratic formula. (3Blue1Brown and Acapella Science described this method in a video on eigenvalues)
PDF not found! 404 (Page Not Found) Error
Ya
Just 10000 ? Think higher man !
Nicolas Heringer that's just a small milestone. I do have videos with over 50000 views but I want to have this video being the first algebra video to be over 10000 views. : )
I've already shared because brazilians loves people singing ! hahaha
lol that's great! thanks
I'M SO DISTRACTED BY THE SUPREME SHIRT
this has now 70 k views and where is him singing the song?
#QuadraticEquation
Another method: shift solve
He spells Ti as Thi
Tic tac to as thic tha tho 😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😊😊😊
Where can I send you my math doubts?
Give your e-mail for that please
U can also solve By new method by Po-Shen-Loh discover in 25 Dec 2019
Good video, but surely you shouldn't be studying complax numbers before you have quadratic equations totally sussed
how old are you ?
x - 3 = 0
x = 3
almost to 10000 views
Now is 5
So basically I need to know at least two different methods(or should I learn all of them..I hate using too many methods for one thing)....one when factorable and one when factoring is not an option? I saw you did some stuff to rearrange the order of the equation....transfer the equal sign from left to right....what is that???! And you also reformed the first problem (looked like what you get after factoring a trinomial) into a normal looking quadratic equation!?!? I understand a quad equation can be factorable or not,but what is it with all the varying appearances?...it's annoying to me...3x^2+ -8- 12=0..........................(3x+5)(2x+5)..........3x^2=6x+9........how many variations are there and why
x + 2 = 20
x = 18
He wore supreme before it was cool.
You got 10000 views. Now sing!
I personally hate the quadratic formula , its very ugly and doesn’t prove student’s ability of solving problems
Misho Okropiridze neither do the other 3 ways
Nearly there
if you wont sing, i will when i have at least 30 subs
you're cute ❤
#linearequation #factoring #factor