2012/019) If a and b are unequal and x^2+ax+b and x2+bx+a have a common factor ,then show that a+b+1=0

they have a common factor x- m

so m^2 + ma + b = 0 ...1
m^2 + mb + a = 0 ..2

subtract 2 from 1

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

m = 1

this is the common factor and putting in any of above equation we get the result