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$α, β$ are roots of equation $3 x 2 − 2 x + 1 = 0$ then the value of $3 α 3 + 3 α 2 β − 2 α 2 + 4 α − 2 α β + 4 β$

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$3$

1 / 3

$2$

$8$

answer is C.

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Detailed Solution

$\begin{array}{l} 3 α^{3} + 3 α^{2} β - 2 α^{2} + 4 α - 2 α β + 4 β \\ = 3 α^{2} (α + β) - 2 α (α + β) + 4 (α + β) \\ = (α + β) (3 α^{2} - 2 α + 4) \\ = \frac{2}{3} (- 1 + 4) = 2 \end{array}$

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