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Question: If \(x = 3 + i,\) then \(x^{3} - 3x^{2} - 8x + 15 =\)...

If x=3+i,x = 3 + i, then x3−3x2−8x+15=x^{3} - 3x^{2} - 8x + 15 =

A

6

B

10

C

– 18

D

– 15

Answer

– 15

Explanation

Solution

Sol. Given that; x−3=ix - 3 = i ⇒ (x−3)2=i2(x - 3)^{2} = i^{2} ⇒ x2−6x+10=0x^{2} - 6x + 10 = 0

Now, x3−3x2−8x+15=x(x2−6x+10)+3(x2−6x+10)−15x^{3} - 3x^{2} - 8x + 15 = x(x^{2} - 6x + 10) + 3(x^{2} - 6x + 10) - 15 =0+0−15=−15.= 0 + 0 - 15 = - 15.