Question

If α and β are the zeros of the polynomial f(x) = 6x² + x ‒ 2, find the value of (α/ β + β / α).

Answer 1

Given: α and β are zeroes of f(x) = 6x² + x – 2

To find: (α/ β + β / α)

α + β = Sum of zeros = -(coefficient of x)/(coefficient of x²) = -1/6

α β = Product of zeros = (constant term)/(coefficient of x²) = -1/3

Now,

(α/ β + β / α) = {(α + β)² – 2αβ) / αβ }

= (1/36 + 2/3) / (-1/3)

= -25/12