Quadratic Equations · Cubic with complex roots

\alpha = 1

and

\beta = 1 + i\sqrt2

, where

i = \sqrt{-1}

are two roots of the equation

x^3 + ax^2 + bx + c = 0

a, b, c \in \mathbb{R}

, then

\displaystyle\int_{-1}^{1}\left(x^3 + ax^2 + bx + c\right)dx

is equal to:

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