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Geometrical Meaning of Zeros of a Polynomial

If α, β, γ ...

Question

If $α, β, γ$ are the zeroes of a cubic polynomial $a x^{3} + b x^{2} + c x + d$ , then the sum of products of the zeroes taken two at a time is equal to

α - β - γ = \frac{c}{a}

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α . β . γ = \frac{c}{a}

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α + β + γ = \frac{- d}{a}

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α β + β γ + α γ = \frac{c}{a}

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Solution

The correct option is D $α β + β γ + α γ = \frac{c}{a}$
Fundamental facts:
If $α, β, γ$ are the roots of cubici equation $a x^{3} + b x^{2} + c x + d = 0$
then $α + β + γ = - \frac{b}{a}$
$α β + β γ + γ α = \frac{c}{a}$
and $α β γ = - \frac{d}{a}$

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