The value of $x^{3} - 5 x^{2} + 33 x - 19$ , where $x - 2 = 5 i$ , is equal to

12

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10

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8

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20

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Solution

The correct option is A $10$
$x = 2 + 5 i$

$(x - 2)^{2} = (5 i)^{2}$

$x^{2} - 4 x + 29 = 0$

Dividing $x^{3} - 5 x^{2} + 33 x - 19$ by $x^{2} - 4 x + 29$ , we get,

$(x^{3} - 5 x^{2} + 33 x - 19) = (x - 1) (x^{2} + 4 x + 29) + 10$

Putting $x = 2 + 5 i$ , we get,

$(x^{3} - 5 x^{2} + 33 x - 19) = (x - 1) (0) + 10$
$= 10$

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