# Bloody Roots

Algebra Level 3

Consider a function $$f(x)$$ such that $$f(2)=f(6)=0$$. Evaluate the sum of all right sentences.

(1) $$f(x) = k(x^2 - 8x + 12), k \in \mathbb{Z}$$

(2) $$f(1) \cdot f(7) \geq 0$$

(4) $$f(f(2)) = f(f(6))$$

(8) $$f(4) \in \mathbb{C}$$

(16) If $$\displaystyle k^{ \displaystyle k^{ ( \cdots) }} = 2$$, then $$f(4 \pm k^2) = 0$$.

(32) $$f^{(2014)}(x) = k, k \in \mathbb{R}$$

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