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Zeroes of a Quadratic Polynomial

Find a cubic ...

Question

Find a cubic polynomial whose zeros are $α, β$ and $γ$ such that $(α + β + γ) = 4, (α β + β γ + γ α) = 1$ and $α β γ = - 6$ .

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Solution

A cubic polynomial whose zeros are $α, β$ and $γ$ is given by
$p (x) = x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x - α β γ$
Thus, the cubic polynomial is
$p (x) = x^{3} - (4) x^{2} + (1) x - (- 6)$
$p (x) = x^{3} - 4 x^{2} + x + 6$

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