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Covalent Bonding in H2, N2 and O2

What are alph...

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What are alpha beta and gamma carbon atoms

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Q. Find a cubic polynomial whose zeros are

α, β

γ

(α + β + γ) = 4, (α β + β γ + γ α) = 1

α β γ = - 6

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 the equation

x^{3} - 3 x + 11 = 0

, what is the equation whose roots are

(α + β), (β + γ)

(γ + α)

∣ ∣ ∣ ∣ ∣ \begin{matrix} β γ & β γ^{'} + β^{'} γ & β^{'} γ^{'} γ α & γ α^{'} + γ^{'} α & γ^{'} α^{'} α β & α β^{'} + α^{'} β^{'} & α^{'} β^{'} \end{matrix} ∣ ∣ ∣ ∣ ∣ = (α β^{'} + α^{'} β) (β γ^{'} - β^{'} γ) (γ α^{'} + γ^{'} α)

α, β, γ

are the roots of

p x^{3} + q x^{2} + r = 0,

then the value of the determinant

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

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