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Q.

How do you find all the real and complex root of the x3 + 8 = 0

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a

x 1 =2, x 2 =1 3 , x 3 =1+ 3  

b

x 1 =3, x 2 =2 3 , x 3 =5+ 3  

c

x 1 =5, x 2 =1 3 , x 3 =1+ 3  

d

x 1 =6, x 2 =1 3 , x 3 =1+ 3   

answer is A.

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Detailed Solution

x3 + 8 = 0
x3 – 23 = 0
(x + 2) (x2 + 22 – 2x)
(x + 2) (x2 + 4 – 2x)
x + 2 = 0
x1 = –2
(x2 – 2x + 4) = 0
x 2,3 = 2± 12 2  
x 2,3 = 2± 1 12 2  
=1± 3 i  
x 1 =2, x 2 =1 3 , x 3 =1+ 3  

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