If ∝ and β are roots of x2 + ax - b = 0 and γ, δ arethe roots of x2 + ax + b = 0, then (α-γ) (β-δ) (α-δ) (β-γ)
4b2
α+β= -a , αβ= -b , γ+δ=-a γδ=b
therefore (α-γ) (β-δ) (α-δ) (β-γ)
=[ αβ-(α+β)γ+γ2][αβ-(α+β)δ+δ2]
(-b+aγ+γ2)(-b+aδ+δ2)
=(-b-b)(-b-b)=4b2