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If , , are the zeroes of the cubic polynomial x^{3} + 3x^{2}

Question

If $α, β, γ$ are the zeroes of the cubic polynomial $x^{3} + 3 x^{2} - x - 2$ , find the values of the expressions given below:
$α + β + γ, α β + β γ + γ α$ and $α β γ$ .

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Emma Discussed

α, β, γ

are the zeroes of the cubic polynomial

x^{3} + 3 x^{2} - x - 2

, find the values of the expressions given below:

α + β + γ, α β + β γ + γ α

and

α β γ

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Text solutionVerified

x^{3} + 3 x^{2} - x - 2

The expression is in the from

a x^{3} + b x^{2} + c x + d

,
then

a = 1, b = 3, c = - 1, d = - 2

∴ α + β + γ = \frac{- b}{a} = \frac{- 3}{1} = - 3

α β + β γ + γ α = \frac{c}{a} = \frac{- 1}{1} = - 1

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

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Question Text	If $α, β, γ$ are the zeroes of the cubic polynomial $x^{3} + 3 x^{2} - x - 2$ , find the values of the expressions given below: $α + β + γ, α β + β γ + γ α$ and $α β γ$ .
Answer Type	Text solution:1
Upvotes	150