existence of solution of a quadratic matrix equation

Question

I have following quadratic matrix equation and I need to find conditions on given matrices A,B,C such that there exists a solution to this equation.

$X^TAX + X^TB + C = 0$

(For e.g. a trivial case is if A,B,C are diagonal matrices. Then this boils down to n quadratic equations in real numbers and we know iff conditions for a solution to exist.)