If factors of $Z^{2} + Z - 6 = 0$ are $Z + a$ and $Z + b$ , then the value of $a^{3} + b^{3}$ is :

- 19

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35

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19

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- 35

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Solution

The correct option is D $19$
$z^{2} + z - 6 = 0$

$\Rightarrow z^{2} + 3 z - 2 z - 6 = 0$

$\Rightarrow z (z + 3) - 2 (z + 3) = 0$

$\Rightarrow (z - 2) (z + 3) = 0$

So, the factors are $(z - 2) & (z + 3)$

$∴ a = - 2, b = 3$

$\Rightarrow a^{3} + b^{3} = {(- 2)}^{2} + {(3)}^{3}$

$= 27 - 8$

$= 19.$

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