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Q.

If $1, w, w^{2}$ are the cube roots of unity and if $α = w + 2 w^{2} - 3$ then $2 [α^{3} + 12 α^{2} + 48 α + 3] =$

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a

$- 62$

b

$- 120$

c

$- 126$

d

$- 61$

answer is D.

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Detailed Solution

$α = ω + 2 ω^{2} - 3 = ω^{2} - 4$

$\Rightarrow ω^{2} = α + 4$

${(α + 4)}^{3} = ω^{6} = 1$

$α^{3} + 12 α^{2} + 48 α + 63 = 0$

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