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Determinant

If 2x3+3x2+...

Question

If ${2 x}^{3} + {3 x}^{2} + 5 x + 6 = 0$ has roots $α, β, γ$ then find $α + β + γ, α, β + β γ + γ α$ and $α β γ$

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Solution

Sum of the roots $α + β + γ = \frac{- 3}{2}$
$α β + β γ + γ α = \frac{5}{2}$
$α β γ = \frac{- 6}{2} = - 3$

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