A quadratic polynomial f(x)=x^{2}+p x+q, with p and q real numbers, is said to be a double-up polynomial if it has two real roots, one of which is twice the other.
(a) If a double-up polynomial f(x) has p=-15, determine the value of q.
(b) If f(x) is a double-up polynomial with one of the roots equal to 4, determine all possible values of p+q.
(c) Determine all double-up polynomials for which p+q=9.