Easy to think , Harder to solve : 2 ( A Challenge for Mr. Jon Haussmann)

Algebra Level 5

Let \(f(x)\) be a monic quartic polynomial. is of the form ,

\(ax^4+bx^3+cx^2+dx+e\)

Such that ,

\(f(1)=0\)

\(f(3)=240\)

\(f(5)=1344\)

\(f(7)=4663\)

If \(f(x)\) has real roots \(\alpha, \beta, \gamma\) and \(\delta\)

Then evaluate the following ,

\(\left ( \sum_{n=1}^{2}\alpha ^{3n}+\beta ^{3n}+\gamma ^{3n}+\delta ^{3n} \right )\)

This problem is original

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