How many real attractive fixed points can a polynomial have?

While the notion of roots of a quadratic polynomial is rudimentary in high school mathematics, that of its fixed points is uncommon. A real or complex number is a fixed point of a polynomial p (x) p (θ) = θ. The fact that the notion of fixed point of polynomials is not commonly covered in high school or undergraduate mathematics is surprising because the relevance of the fixed points of a quadratic can be demonstrated easily via iterative methods for the approximation of such numbers as, when the quadratic formula offers no remedy.