An algebra problem by Vishwesh Kumar
Algebra
Level
2
Consider the 2 functions: \(f\left( x \right) =x^{ 3 }+ax^{ 2 }+bx+c\\ g\left( x \right) =x^{ 3 }+bx^{ 2 }+cx+a\)
Given:
(i) f(1)=0
(ii) roots of g(x) are squares of roots of f(x)
Find \(a^{ 2013 }+b^{ 2013 }+c^{ 2013 }\)
This question was asked in Regional Mathematics Olympiads 2013 of class 10th
by
Vishwesh Kumar