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If $α, β, 1$ are roots of $x^{3} - 2 x^{2} - 5 x + 6 = 0 (α > 1)$ then $3 α + β =$

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Detailed Solution

x^{3} - 2 x^{2} - 5 x + 6 = 0

Roots are $α, β, 1$

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$x^{3} - 2 x^{2} - 5 x + 6 = (x - 1)$ $(x^{2} - x - 6)$

$x^{2} - x - 6 = 0$

$(x - 3) (x + 2) = 0$

roots are $3, - 2$

$3 α + β = 3 (3) + (- 2) = 7$

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