Explanation:

Given that (x+2) is a common factor of x²+ax+b and x²+bx+a
Let f(x) = x²+ax+b
And g(x) =x²+bx+a
Let p(x) = x+2 this means x+2 = 0
=>x = - 2, so -2 is a zero of f(x) and g(x)
Therefore ax²+ab+b=(−2)2−2a+b=4−2a+b and
x²+bx+a=(−2)2− 2b+a
Both polynomials are same
Thus,
4-2a+b – 4 -2b+a
=> b+2b = a+2a => 3a = 3b => 3a/3b=1
=> a:b = 1:1