If α and β, α and γ, α and δ are the roots of the equations ax2+2bx+c=0, 2bx2+cx+a=0 and cx2+ax+2b=0 respectively, where a, b and c are positive real numbers, then α+α2=

Here α+β=-2baγ+α=-c2b, α+δ=-acand αβ=ca, αγ=a2b, αδ=2bc⇒α+δ=-1αβ, α2β+αβδ=-1    ...(i)⇒α+β=-1αγ, α2γ+αβγ=-1     ...(ii)⇒α+γ=-1αδ,α2δ+αβγ=-1   ...(iii)Solve equations (i), (ii) and (iii), we get α=-1