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.
by
Vishwak Srinivasan