If $α, β, γ$ $alpha,beta,gamma$ and $δ$ $delta$ are roots of $x^{4} + 9 x^{2} + 7 x - 8 = 0$ $x^4+9x^2+7x-8=0$ , what is the value of $(α + β) (γ + δ) + α \cdot β + γ \cdot δ$ $(alpha+beta)(gamma+delta)+alphabeta+gammadelta$ ?

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If $α, β, γ$ $alpha,beta,gamma$ and $δ$ $delta$ are roots of $x^{4} + 9 x^{2} + 7 x - 8 = 0$ $x^4+9x^2+7x-8=0$ , what is the value of $(α + β) (γ + δ) + α \cdot β + γ \cdot δ$ $(alpha+beta)(gamma+delta)+alphabeta+gammadelta$ ?

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Answer 1 · 2016-05-26T11:53:18

$(α + β) (γ + δ) + α \cdot β + γ \cdot δ = 9$ $(alpha+beta)(gamma+delta)+alpha*beta+gamma*delta=9$

Explanation:

As $α, β, γ$ $alpha,beta,gamma$ and $δ$ $delta$ are roots of $x^{4} + 9 x^{2} + 7 x - 8 = 0$ $x^4+9x^2+7x-8=0$

We have $(x - α) (x - β) (x - γ) (x - δ) \Leftrightarrow x^{4} + 9 x^{2} + 7 x - 8 = 0$ $(x-alpha)(x-beta)(x-gamma)(x-delta)hArrx^4+9x^2+7x-8=0$

or $x^4-(alpha+beta+gamma+delta)x^3+(alpha*beta+alpha*gamma+alpha*delta+beta*gamma+beta*delta+gamma*delta)x^2-(alpha*beta*gamma+alpha*gamma*delta+alpha*beta*delta+beta*gamma*delta)x+alphabetagammadeltahArrx^4+9x^2+7x-8$ (A)

As $(alpha+beta)(gamma+delta)+alpha*beta+gamma*delta=alpha*gamma+alpha*delta+beta*gamma+beta*delta+alpha*beta+gamma*delta$

comparing the coefficients of $x^2$ in (A)

$(alpha+beta)(gamma+delta)+alpha*beta+gamma*delta=9$

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If $α, β, γ$ $alpha,beta,gamma$ and $δ$ $delta$ are roots of $x^{4} + 9 x^{2} + 7 x - 8 = 0$ $x^4+9x^2+7x-8=0$ , what is the value of $(α + β) (γ + δ) + α \cdot β + γ \cdot δ$ $(alpha+beta)(gamma+delta)+alphabeta+gammadelta$ ?

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Explanation:

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If alpha,beta,gammaα,β,γalpha,beta,gamma and deltaδdelta are roots of x^4+9x^2+7x-8=0x4+9x2+7x−8=0x^4+9x^2+7x-8=0, what is the value of (alpha+beta)(gamma+delta)+alpha*beta+gamma*delta(α+β)(γ+δ)+α⋅β+γ⋅δ(alpha+beta)(gamma+delta)+alpha*beta+gamma*delta?

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Explanation:

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If $α, β, γ$ $alpha,beta,gamma$ and $δ$ $delta$ are roots of $x^{4} + 9 x^{2} + 7 x - 8 = 0$ $x^4+9x^2+7x-8=0$ , what is the value of $(α + β) (γ + δ) + α \cdot β + γ \cdot δ$ $(alpha+beta)(gamma+delta)+alphabeta+gammadelta$ ?