If $α, β$ and $γ$ are the zeroes of the polynomial $f (x) = a x^{3} + b x^{2} + c x + d$ , then $\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}$ is _____.

$\frac{c}{d}$

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$\frac{a}{d}$

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$- \frac{c}{d}$

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$- \frac{b}{a}$

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Solution

The correct option is C
$- \frac{c}{d}$

Given $α, β$ and $γ$ are the zeroes of the polynomial $f (x) = a x^{3} + b x^{2} + c x + d$

$\frac{1}{α} + \frac{1}{β} + \frac{1}{γ}$

$= \frac{β γ + α γ + α β}{(α β γ)}$ $= \frac{(\frac{c}{a})}{(- \frac{d}{a})}$ $= - \frac{c}{d}$

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