If `alpha,beta,gamma` are the zeros of the polynomial `f(x)=x^3-p x^2+q x-r ,` then `1/(alphabeta)+1/(betagamma)+1/(gammaalpha)=`
(a) `r/p` (b) `p/r` (c) `-p/r` (d) `-r/p`

Explanation

Given that `alpha,beta,gamma` are the zeroes of the polynomial `f(x)=x^3-p x^2+q x-r`.

`therefore alpha + beta + gamma = p`

`alpha beta + beta gamma + gamma alpha = q`

`alpha beta gamma = r`

`therefore 1/(alpha beta)+1/(beta gamma)+1/(gamma alpha)`

`= (alpha + beta + gamma)/(alpha beta gamma)`

`= p/r`

Hence, the correct answer is option B.