Question

If α &β are zeroes of f(x)=X square +X -2, find 1/α - 1/β

Answer 1

1/α - 1/β= β-α/βα Take LCM

now α+β=-1 and βα=-2

(α+β)^2-(β-α)^2=4βα

1-(β-α)^2=-8

(β-α)^2=9

(β-α)=+3 and -3

so required value is 3/2 & -3/2