Question

if the equation x^2+ax+b=0 and x^2+bx+a=0 have a common root then prove that a+b=-1

Answer 1

Answer:

Step-by-step explanation:

Since both the equations have common root..let us think that common root as ‘N’.  

So N²+aN+b=0        >>eq-1

and N²+bN+a=0       >>eq-2

Both the results will be equal to ‘0’ bcoz N Divides both of them..

So N²+aN+b = N² +bN+a

aN + b = bN+a

aN - bN = a-b

N(a-b)= a-b

And finally N=1

Substituting N value in any of the equation 1 or 2

Then we will get

1+a+b= 0

so >> a+b = -1

..hence proved