Question

if ax^2+bx+c and bx^2+ax+c have a common factor x+1 then show that c=0 and a=b

Answer 1

ax^2+bx+c=0.......eq.1
bx^2+ax+c=0....eq.2
common factor x+1=0 then x=-1
in eq.1 a(-1)^2+b(-1)+c=0then a-b+c=0...eq.3
in eq.2b(-1)^2+a(-1)+c=0thenb-a+c=0...eq.4
subtract eq.3-eq.4
a-b+c=0
-a+b+c=0 then 2a-2b=o then a-b=0
a=b after put a=bin eq.3 then b-b+c=0then c=0 hence a=b and c=0 proved