Discussion Forum



1)

The sum of the complex roots of the equations $(x-1)^{3}+64$=0 is 


A) 6

B) 3

C) 6i

D) 3i

Answer:

Option A

Explanation:

We have,

  $(x-1)^{3}+64$=0 

 $\Rightarrow$           $(x-1)^{3}=-64$           

 $\Rightarrow$                $(x-1)^{3}=(-4)^{3}$

 $\Rightarrow$        x-1=-4,-4w,-4w2

 $\Rightarrow$                 x=-3,-4w+1,-4w2+1

 Complex roots of the equations are

  -4w+1,-4w2+1

Sum of complex roots are

   -4w+1-4w2+1=-4(w+w2)+2

  $=-4(-1)+2=4+2=6$    $[\because1+w+w^{2}=0]$