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f(x) = x^3 + 3x^2 - 1 with roots a,b,c find a^3 + b^3 + c^3, a^2b + b^2c + c^2a

Source: Canada Repêchage 2019/3 CMOQR

March 1, 2020
polynomialalgebraroots

Problem Statement

Let f(x)=x3+3x2āˆ’1f(x) = x^3 + 3x^2 - 1 have roots a,b,ca,b,c. (a) Find the value of a3+b3+c3a^3 + b^3 + c^3 (b) Find all possible values of a2b+b2c+c2aa^2b + b^2c + c^2a
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