Given: α and β are zeroes of f(x) = x2 + x – 2
To find: (1/α – 1/β)
α + β = Sum of zeros = -(coefficient of x)/(coefficient of x2) = -1
α β = Product of zeros = (constant term)/(coefficient of x2) = -2
Now,
(1/α – 1/β) = (β – α)2) / αβ
= (β + α)2 – 4αβ) / (αβ)2
= 9/ 4