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 87272 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 $@ty@m123 last updated on 03/Apr/20

S u b t r a c t t h e t w o e q u a t i o s .

(a x + b) - (b x + a) = 0

\Rightarrow (a - b) x - (a - b) = 0

\Rightarrow x = 1 i s t h e c o m m o n r o o t .

P u t x = 1 i n f i r s t (o r s e c o n d) e q u a t i o n .

\Rightarrow a + b = - 1 .

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

y o u m e a n t a + b = - 1 s i r .

Commented by $@ty@m123 last updated on 03/Apr/20

T h a n k s f o r c o r r e c t i o n .