Given: α and β are zeroes of f(x) = 5x2 ‒ 7x + 1
To find: (1/α + 1/β)
α + β = Sum of zeros = -(coefficient of x)/(coefficient of x2) = 7/5
α β = Product of zeros = (constant term)/(coefficient of x2) = 1/5
Now,
(1/α + 1/β) = (α + β) / αβ
= 7/5 x 5/1
= 7