# Cubic Arithmetic Progressions

Algebra Level 3

The cubic equation $$f(x) = x^3 - 12 x^2 + 34 x - N$$ has roots that are in an Arithmetic Progression. What is the value of $$N$$?

Details and assumptions

3 numbers form an Arithmetic Progression if they are of the form $$a, a+d, a+2d$$ for some (possibly complex) values $$a$$ and $$d$$.

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