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the roots of the eqation (x-1)^3+8=0 are According to my Referance Book are -1,1-2w,1-2w^2 So please reply how is it

the roots of the eqation (x-1)^3+8=0 are According to my Referance Book are -1,1-2w,1-2w^2


So please reply how is it

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear manan

earlier i have replied to this problem ,at that time u have not maintion the complex root so i was only dealing real roots.

for complex root you have to solve it

  (x-1)^3+8=0

 (x-1)3+23=0

 

you can factorise it easly with the formula

 a3 + b3 = (a+b)(a+bw)(a+bw2)    where w is the cube root of unity

 {(x-1)+2}{(x-1) +2w}{(x-1) +2w2} =0

 ( x+1)(x +2w-1)(x +2w2 -1) =0

  it gives the root  1,1-2w,1-2w^2

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Badiuddin

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