# A Not-So-Special Cubic Function

Algebra Level 5

Let $$f(x)$$ be a monic cubic function with the following properties:

• For any line $$L(x)$$ such that $$L(2)=2$$ that intersects $$f(x)$$ at three distinct points $$(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3}),$$ the sum $$x_{1}+x_{2}+x_{3}=2$$.

• For any quadratic function $$P(x)$$ such that $$P(0)=0$$ that intersects $$f(x)$$ at three distinct points $$(x_{4},y_{4}),(x_{5},y_{5}),(x_{6},y_{6}),$$ the product $$x_{4}x_{5}x_{6}=-3$$.

• $$f(2)=17$$

Find the value of $$f(5)$$.

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