TS EAMCET 10-Sep-2020 Shift 1 Solved Paper

Given
α1,β1,γ1,δ1 are the roots of equation
ax4+bx3+cx2+dx+e=0 and
α2,β2,γ2,δ2 are the roots of equation
ex4+dx3+cx2+bx+a=0
∴ Clearly,
α1,β1,γ1,δ1 are the reciprocal of roots of
ax4+bx3+cx2+dx+e=0
Also, δ1>γ1>β1>α1>0
and δ2>γ2>β2>α2>0
∴δ1 and α2 are reciprocal
Similarly γ1 and β2, γ2 and β1 and α1 and δ2 are reciprocal
α1−δ2=2
and δ1−α2=4
δ1−‌

1

δ1

=4=δ12−4δ1−1=0
∴α1 and δ1 are roots of
ax4+bx3+cx2+dx+e=0
Put x=1,
8=a+b+c+d+e