  Every linear, quadratic or cubic polynomial having all real zeros is the
derivative of a polynomial having all real zeros. The statement is false for
higher degree polynomials. In particular, not every fourth degree polynomial
with real zeros is the derivative of a polynomial having all real zeros. We
derive a necessary and sufficient condition for a quartic polynomial to be the
derivative of a polynomial having all real zeros. This condition is a single
quadratic form inequality involving the zeros of the quartic polynomial.
