Cubic Arithmetic Progressions
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 \(d\).