Complex Numbers : Roots of a quadratic equation - conjugate pairs : ExamSolutions
Вставка
- Опубліковано 6 жов 2024
- Tutorial on complex numbers. I show you how to find the roots of a quadratic equation (conjugate pairs).
UA-cam CHANNEL at / examsolutions
EXAMSOLUTIONS WEBSITE at www.examsoluti... where you will have access to all playlists covering pure maths, statistics and mechanics.
/ examsolutions.net
NEW INSTAGRAM: / examsolutionsguy
TWITTER: / examsolutions
THE BEST THANK YOU: www.examsoluti...
Your Voice, Your Accent...
How was your life in these 8 years
@@senthilpuliadi6599 holy shit what a question lmaooo that kind of question stops someone dead in their tracks and makes them think about everything.. hopefully shes fine
Ya it’s fun
I really hope she replies
she needs to reply to this, it is a great question...I really wonder how she is now. Man, how the time passes...
Sub x=3-i into the equation and then equate real and imag. parts. to find a, and b. For the other root you could then sub x=ki into the equation and compare real and imag. parts
This is soo understandable
Thank you very much Sir!
Thanks for watching.
your the best :)
Thanks sir, that was very helpful
@DevilVu Have you looked at my first video on complex numbers. It explains it there.
Because if this is equal to zero then x=a or x=b. This was the line before where I have the roots.
thank you sir i am from india (bharat )
nice
Sir , why , (x-a)(x-b) ? is it because ,this is how quadratic equation is formed ? also why both signs are negative ?
Bc if a is one of the roots then x-a=0, same with b (x-b=0)
This will result in x=a (and x=b) if you take it to the other side .
Why is (x-α)(x-β) = 0 implied? I've seen you solve for the roots, before. Couldn't you also just use (x+α)(x-β) = 0 or (x+α)(x+β) = 0? I know two minus signs would make it pretty easy to solve. Do these other forms somehow not always give rise to a quadratic equation?
isnt there a simpler way of working it out in the text book?
takmaps yes, he didn’t explain it
You didn’t explain the faster way of solving these questions which is adding the roots and multiplying them out
ExamSolutions
Hi sir, may I ask you since the equation takes the form of (x-a)(x-b), surely if x=a then x=b and hence a=b too right? I am still unsure why the equation is (x-a)(x-b).
And finally sir, for both questions, I worked out a+b and ab and then subbed the values in the equation x^2 - (a+b)x +ab, by expanding (x-a)(x-b) - this gets the same answer as you did, so is it acceptable to use either method.
Regards sir!
In answers to your first question a=b then not necessarily. If (x-3)(x-2)=0 then x=3 or x=2. If I had (x-3)(x-3)=0 then x=3 in both cases.
As for your second question. Was your alternative method correct, then yes it was.
Since i^2 = -1 and -1 x 16 = -16, that means -16 can be simplified to 16i^2. If you take the square root of this, 16 square rooted is 4 (or -4) and i^2 square rooted is i. So, the roots of -16 are 4i and -4i.
-4i will not be the case
Bcoz √anything will always give positive value..... √-16 = 4i
You should have just used sum/product approach as one would with surd conjugates.
Yes I could have done but it was intentional to show it this way as some students may not have studied that approach at this point. Like many maths problems there can often be more than one way of doing a solution and that is an alternative but I take your point. Thanks.
@@ExamSolutions_Maths No problem, I still used it to introduce students to the ideas.
Sir when you multiply -3i and 3i, why do you get 9
-3 x 3 = -9 and i multiplied by i is -1 so 9 x (-1) = 9
What about if there is a 3rd root we have to find, or is this only in cubics? This is useful to know, and when i factorise the quadratic at the end it leads me back to the same roots of the original.
I know it's been 7 months since you asked this question, but yes quadratic means that there can be 2 real, or 2 imaginary (like in the video), or two same roots. In cubic, however, as you thought there can be 3 roots at maximum.
where the hell did you get i from mate? 1:57
how is root -16 = 4i again?
root -16= root -1 * root 16=i*4=4i
@@greenpanda4475 You were 6 years late..
@@fbdjwjflac sumthing is betterbrhan nuthing XD