If α , β and γ are the zeroes of the polynomial f ( x ) = a x 3 + b x 2 + c x + d , then 1 α + 1 β + 1 γ is _____. Options: A . &nbspcd B . &nbspad C . &nbsp−cd D . &nbsp−ba

If α,β and γ are the zeroes of the polynomial f(x)=ax3+bx2+cx+

Question

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 _____.

Options:

A . cd

B . ad

C . −cd

D . −ba

Answer: Option C
:
C
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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