# Cyclic summation of roots of a cubic

Algebra Level 4

$\large 2x^3 + x^2 - 7 = 0$

If $\alpha, \beta, \gamma$ are the roots of the above equation, evaluate

$\large \left | \displaystyle \sum_{\text{cyc}} \left( \dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} \right )\right|$

Note

• $|z|$ is the absolute value of $z$

• $\displaystyle \sum_{\text{cyc}}$ means cyclic summation.

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