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Nature of Roots

If α, β and γ...

Question

If α, β and γ are the real roots of a³ − 6a²+ 3a + 1 = 0, determine the sum of possible values of α²β + β²γ + γ²α.

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Similar questions

α, β, γ

are the roots of

x^{3} + a x + b = 0

(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =

α, β, γ

are the roots of

x^{3} + q x + r = 0

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

α, β, γ

are the roots of

a x^{3} + b x^{2} + c x + d = 0

∣ ∣ ∣ ∣ ∣ \begin{matrix} α & β & γ β & γ & α γ & α & β \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

α \neq β \neq γ

, then find the equation whose roots are

α + β - γ, γ + α - β, β + γ - α

α

β

γ

are the roots of

x^{3} + a x^{2} + b = 0

, then the value of determinant

Δ

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α & β & γ β & γ & α γ & α & β \end{matrix} ∣ ∣ ∣ ∣ ∣

.

α, β, γ

x^{3} - x^{2} - 1 = 0

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

.

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