# The importance of discriminant

Algebra Level 3

$\large \begin{cases} a+b+c &= 2017 \\ ax^{2}+a^{2}x+a^{3} &= 0 \\ b^{3}x^{2}+b^{2}x+b &= 0 \\ x^{2} + cx+ 2017 &= 0 \end{cases}$

Given that $$a$$, $$b$$ and $$c$$ are real numbers and let $$\alpha$$ and $$\beta$$ be real roots of $$x$$ which satisfy the system of equations above. Find $$| \alpha+\beta |$$.

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