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alpha and beta are the roots of the equation x^2-x+1=0 then the equation for the roots alpha^2018 and beta^2018

alpha and beta are the roots of the equation x^2-x+1=0 then the equation for the roots  alpha^2018 and beta^2018

Grade:8

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
its root will be 
alpha = – w
beta = – w^2
 
now
 
a^2018 = (– w)^2018 = w^2018 = w^2
 
bet^2018 = (– w^2)^2018 = w^4036 = w
 
now sum = w + w^2 = – 1
product = w * w^2 = w^3 = 1
 
hence equation will be 
 
x^2 + x + 1 =0
 
Regards
Arun

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