Cubic Arithmetic Progressions

Algebra Level 3

The cubic equation f(x)=x312x2+34xN f(x) = x^3 - 12 x^2 + 34 x - N has roots that are in an Arithmetic Progression. What is the value of NN?

Details and assumptions

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

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