AP EAPCET 20-Aug-2021 Shift 2 Paper

Given, equations are
x2+ax+b=0 ...(i)
x2+bx+a=0 ...(ii)
Let α be common root of Eqs. (i) and (ii), then
α2+aα+b=0 ...(iii)
α2+bα+a=0 ...(iv)
Compare Eqs. (iii) and (iv), we get
α2+aα+b=α2+bα+a
⇒α(a−b)=(a−b)
⇒α=1
Common root =1
From Eq. (iii), we get
1+a+b=0
⇒a+b=−1