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If , , are the zeroes of the cubic polynomials x^{3} + 5x^{2}

Question

If $α, β, γ$ are the zeroes of the cubic polynomials $x^{3} + 5 x^{2} + 4$ , find the values of the exoressions given below:
$α + β + γ, α β + β γ + γ α$ and $α β γ$ .

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Charlotte Discussed

α, β, γ

are the zeroes of the cubic polynomials

x^{3} + 5 x^{2} + 4

, find the values of the exoressions given below:

α + β + γ, α β + β γ + γ α

and

α β γ

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Text solutionVerified

x^{3} + 5 x^{2} + 4

The expression is in the form

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

then

a = 1, b = 5, c = 0, d = 4

∴ α + β + γ = \frac{- b}{a} = \frac{- 5}{1} = - 5

α β + β γ + γ α = \frac{c}{a} = \frac{0}{1} = 0

α β γ = \frac{- d}{a} = \frac{- 4}{1} = - 4

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Question Text	If $α, β, γ$ are the zeroes of the cubic polynomials $x^{3} + 5 x^{2} + 4$ , find the values of the exoressions given below: $α + β + γ, α β + β γ + γ α$ and $α β γ$ .
Answer Type	Text solution:1
Upvotes	150