Question

If ax²+bx+c and bx²+ax+c have a
common factor X+1 then show that
C=0 and a=b.​

Answer 1

Answer:

Given,

ax^2+bx+c and bx^2+ax+c have common factor x+1

x+1=0

x=-1

substitute x in the above equation

a(-1)^2+b(-1)+c=0

a-b+c=0:eq.1

b(-1)^2+a(-1)+c=0

b-a+c=0:eq2

from equation 1 and 2

a-b+c=0

-a+b+c=0

--------------

2c=0

c=0/2

c=0

substitute c in equation 1

a-b+0=0

a=b

therefore hence showed