If $α, β, γ$ are the zeroes of the cubic polynomial $4 x^{3} + 8 x^{2} - 6 x - 2$ , find the values of the expressions given below:
$\alpha +\beta + \gamma , \alpha \beta + \beta \gamma + \gamma \alpha $a n d$ \alpha \beta \gamma $.

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Solution

$4 x^{3} + + 8 x^{2} - 6 x - 2$

The expression in in the form
$a x^{3} + b x^{2} + c x + d$ ,
then
$a = 4, b = 8, c = - 6, d = - 2$

$∴ α + β + γ = \frac{- b}{a} = \frac{- 8}{4} = - 2$

$∴ α β + β γ + γ α = \frac{c}{a} = \frac{- 6}{4} = \frac{- 3}{2}$

$α β γ = \frac{- d}{a} = \frac{- (- 2)}{4} = \frac{1}{2}$

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