Let r>0 be a real number. We call a monic polynomial with complex coefficients r-good if all of its roots have absolute value at most r. We call a monic polynomial with complex coefficients primordial if all of its coefficients have absolute value at most 1.
a) Prove that any 1-good polynomial has a primordial multiple.
b) If r>1, prove that there exists an r-good polynomial that does not have a primordial multiple.Proposed by Pranjal Srivastava Polynomialsalgebrapolynomial