Cyclic summation of roots of a cubic

Algebra Level 4

2x3+x2−7=0\large 2x^3 + x^2 - 7 = 0

If α,β,γ\alpha, \beta, \gamma are the roots of the above equation, evaluate

∣∑cyc(αβ+βα)∣\large \left | \displaystyle \sum_{\text{cyc}} \left( \dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} \right )\right|

Note

  • ∣z∣|z| is the absolute value of zz

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

Vishwak Srinivasan by Vishwak Srinivasan
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