Question

If α, β, γ are the zeros of the polynomial f(x) = x³ – px² + qx – r, then \(\frac{1}{αβ}\) + \(\frac{1}{βγ}\) + \(\frac{1}{\gamma \alpha}\) =

A. \(\frac{r}{p}\)

B. \(\frac{p}{r}\)

C. - \(\frac{p}{r}\)

D. - \(\frac{r}{p}\)

Answer 1

Given,

f(x) = x³ – px² + qx – r

α, β and y are the Zeros,

α + β + y = – p

αβ + βy + yα = – q

αβy = – r

1/αβ + 1/βy + 1/yα = p/r