The endosymbiotic theory concerns the origins of mitochondria and chloroplasts, which are organelles of eukaryotic cells. According to this theory, these originated as prokaryotic endosymbionts, which came to live inside eukaryotic cells.he theory postulates that the mitochondria evolved from aerobic bacteria (probably proteobacteria, related to the rickettsias), and that the chloroplast evolved from endosymbiotic cyanobacteria (autotrophic prokaryotes).
The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient a n = 1.
In the same way we saw that only the square roots of square numbers are rational, we could prove that only the nth roots of nth powers are rational. Thus, the 5th root of 32 is rational, because 32 is a 5th power, namely the 5th power of 2. But the 5th root of 33 is irrational. 33 is not a perfect 5th power.