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If 1, 2, 3 and 4 are the roots of the equation $x^{4} + a x^{3} + b x^{2} + c x + d = 0$ , then $a + 2 b + c =$

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Detailed Solution

$\begin{array}{l} x^{4} + a x^{3} + b x^{2} + c x + d = 0 \\ a = - (α + β + γ + δ) = - (1 + 2 + 3 + 4) = - 10 \\ c = \sum α β γ = - (6 + 8 + 12 + 24) = - 50 \\ d = \sum β γ δ = 24 \\ a + 2 b + c = - 10 + 70 - 50 = 10 \end{array}$

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