If-the-equations-x-2-ax-b-0-and-x-2-bx-a-0-have-a-common-root-then-the-numerical-value-of-a-b-is-

Question Number 87275 by unknown last updated on 03/Apr/20

If the equations x^{2} + a x + b = 0 and

x^{2} + b x + a = 0 have a common root,

then the numerical value of a + b is

Answered by Rio Michael last updated on 03/Apr/20

let the common root be α

\Rightarrow α^{2} + α a + b = 0

also α^{2} + α b + a = 0

\Rightarrow when x = α

α^{2} + α a + b = α^{2} + α b + a

α a + b = α b + a

α a - α b = a - b

α (a - b) = (a - b) \Rightarrow α = 1

from x^{2} + a x + b = 0 at x = 1

1 + a + b = 0 \Rightarrow a + b = - 1

please check sir

Commented by mr W last updated on 03/Apr/20

p l e a s e {d o n}^{'} t a n s w e r a q u e s t i o n w h i c h

i s r e d m a r k e d! i t i s r e d m a r k e d b e c a u s e

i t s h o u l d b e r e m o v e d .

Commented by Rio Michael last updated on 03/Apr/20

really sir ? sorry i {didn}^{'} t know, is there some group

rules for that ?

Commented by mr W last updated on 03/Apr/20

A p o s t i s r e d m a r k e d t h r o u g h t h e

m e n u “ F l a g p o s t a s {i n a p p r o p r i a t e}^{″} .

u s u a l l y b e c a u s e i t i s n o n s e n s e,

r e p e a t e d . t h e r e a r e n o s p e c i a l r u l e s

i n t h i s f o r u m . t h a t m e a n s w e s h o u l d

k e e p t h e f o r u m c l e a n, b y e a c h o f u s .

Commented by Rio Michael last updated on 04/Apr/20

you are right sir, and am greatful to you