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If x = 3 + i,...

Question

If x = 3 + i, then $x^{3} + 3 x^{2} - 8 x + 15$ =
[UPSEAT 2003]

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Solution

The correct option is D -15
x = 3 + i $\Rightarrow$ x - 3 = i
$\Rightarrow x^{2} - 6 x + 10 = 0 \Rightarrow x^{3} - 3 x^{2} - 8 x + 15$
$= x (x^{2} - 6 x + 10) + 3 (x^{2} - 6 x + 10) - 15$
= x(0) + 3(0) - 15 = -15.

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