If zeros of the polynomial `f(x)=x^3-3p x^2+q x-r` are in A.P., then (a) `2p^3=p q-r` (b) `2p^3=p q+r` (c) `p^3=p q-r` (d) None of these

Explanation

Let `alpha, beta and gamma` be the zeros of the polynomial `f(x)=x^−3px^2+qx−r`.

`f(x)=x^3−3px^2+qx−r`

`=(x−alpha)(x− beta )(x− gamma)`

`=x^3−(alpha + beta + gamma)x^2+(alpha beta + beta gamma + gamma alpha)x− alpha beta gamma`

Equating the coefficients of `x^2`,

`−( alpha + beta + gamma)=−3p`

` alpha + beta + gamma =3p ……….(1)`

Given that ` alpha, beta and gamma` are in A.P. Let d be the common difference of terms of the AP.

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