Question

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Answer 1

If the quadratic equations :-
\[\huge x ^{2} + bx + c =0\]
\[\huge x ^{2} + cx + b = 0 \] \[\huge b \neq c\]
have a common root then prove that their uncommon are the roots of the equation
\[\huge x ^{2} +x+bc=0\]

Answer 2

uncommon roots

Answer 3

Let the common root be \(\alpha\).\[\alpha^2 +b\alpha + c = 0 \]\[\alpha^2 + c\alpha + b=0\]So\[b\alpha + c = c\alpha + b\]\[(b - c)\alpha = b - c\]\[\alpha = 1\]

Answer 4

Bas, ab toh ho gaya :)

Answer 5

yes

Answer 6

haan then find product of roots in both cases and u will get
x^2 -(b+c)x +bc =0
and then as alpha =1 we get b-c=-1
so proved

Answer 7

Sahi, sahi.

Answer 8

are you preparing for iit

Answer 9

Pehli equation ka root \(c\) hai. Product of roots se dekh lo.
Doosri ka similarly \(b\) hai, by product of roots.

Toh uncommon roots \(b,c\) hain.

Answer 10

Aur sum of roots se jo aapne bola.

Yes, I'm preparing for IIT.

Answer 11

good !

Answer 12

Which class are you in?

Answer 13

apke syllabus me hai yeh sab

Answer 14

I am in 8 th

Answer 15

u?

Answer 16

You earlier said that you were in 11th. :\

I'm in 10th.

Answer 17

I use my elder brother's account

Answer 18

Oh, nice.

Answer 19

He dosen't even know that

Answer 20

Aaj advanced ka paper tha

Answer 21

Achcha.

Answer 22

Are you really in 8th?

Answer 23

haan , par ye syllabus me nahin he hamare

Answer 24

I am learning from web site

Answer 25

Humare bhi nahi. I think ye 11th mein aata hai.

Answer 26

I will create a new account tommorow for myself

Answer 27

Apne kaha se yeh sikha

Answer 28

web site se kya

Answer 29

Nahi, coaching.

Answer 30

acha

Answer 31

apko calculus aata hai i don't even know the C of calculus

Answer 32

Thoda thoda aata hai. Coaching mein itna nahi karwaya, bas basics karwaye they physics class mein. Maths mein abhi nahi padha.

Answer 33

easy hai kya calculus

Answer 34

chalo bye ! c u tommorow

Answer 35

I will tell you my username tommorow

Answer 36

OK, bye bye.