Question

If alpha and beta are zeroes of polynomial px = 5x square + 5x + 1 then find the value of alpha -1 + beta -1

Answer 1

The given polynomial is:

p(x) = 5x² + 5x + 1

Since α and β are the zeroes of p (x),

α + β = - 5/5

⇒ α + β = - 1 ...(1)

and

αβ = 1/5 ...(2)

Now, α^(- 1) + β^(- 1)

= 1/α + 1/β

= (β + α)/(αβ)

= (- 1)/(1/5)

= - 5