# 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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