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Question

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anonymous · Answer

$$\huge x ^{2}-4x +5 =0$$
$$\huge x ^{2} +ax + b =0 $$
These equations have a common root 
Then find a and b 


{THIS IS THE QUESTION AS WRITTEN IN THE TEXTBOOK , THERE ARE NO CHANGES}

anonymous · Answer

@ganeshie8

anonymous · Answer

The first equation has imaginary roots .

ganeshie8 · Answer

good observation !

ganeshie8 · Answer

and they always come in pairs, so...

anonymous · Answer

yeah both roots are imaginary

ganeshie8 · Answer

yes and cant we also conclude a=-4 and b=5 ?

anonymous · Answer

The second one also has imaginary roots . But how can we say that the uncommon root is equal

ganeshie8 · Answer

say the common root is $\large a + bi$

anonymous · Answer

It is given in the question one root is common
But,
For the equations to be equal
both the roots must be common
So,
How do we know the uncommon root is "common"

anonymous · Answer

ok

ganeshie8 · Answer

since $\large a+bi$ is one root, its conjugate pair $\large a-bi$ wll also be a root

anonymous · Answer

yes

ganeshie8 · Answer

and since $\large a+bi$ is a root for both equations, 
the conjugate pair $\large a-bi$ will also be a root for both equations

ganeshie8 · Answer

assuming $a$ and $b$ are real *

ganeshie8 · Answer

Sorr, I must have used different letters... but i hope u see the point :)

anonymous · Answer

Yes i get your point!

anonymous · Answer

Dosen't matter i figured it out

ganeshie8 · Answer

good :)

anonymous · Answer

Thank you

parthkohli · Answer

Hey, I'm also studying Theory of Quadratic Equations right now.  Can you tag me whenever you have an interesting question?  It would make for practice.  :D

anonymous · Answer

Cool me isse ek website se learn kar raha hoon i have very good question i solved it but do you want to try it i will post it then Mee https://www.youtube.com/watch?v=7vwCbxzgwBY&index=8&list=PL3Wi397dlS-FDkJtl0hgJt-fnvSyeplZi iss website se learn kar raha hooon

parthkohli · Answer

Oh, come to the math chat... we can discuss these if you want.

parthkohli · Answer

MIT 18.311 chat.

anonymous · Answer

ok

anonymous · Answer

wait

parthkohli · Answer

Kahan gaye?  :|

anonymous · Answer

Can u give the link

anonymous · Answer

Sorry net gaya tha

parthkohli · Answer

http://openstudy.com/study#/groups/MIT%2018.311%20Principles%20of%20Applied%20Mathematics