Question

If α and β are the zeros of the polynomial f(x) = x² + px + q, then a polynomial having $\frac{1}{\mathrm{\alpha }}\mathrm{and}\frac{1}{\mathrm{\beta }}$ is its zero is

(a) x² + qx + p
(b) x² − px + q
(c) qx² + px + 1
(d) px² + qx + 1

Answer 1

Let and be the zeros of the polynomial.Then,

And

Let S and R denote respectively the sum and product of the zeros of a polynomial

Whose zeros are and .then

Hence, the required polynomial whose sum and product of zeros are S and R is given by

So

Hence, the correct choice is