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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