For the quadratic equation: x + px + q = 0, it is given that p and q are its root. As well as for the given quadratic equation: we have, a = 1, b = p and c = q. ⇒ Sum of the roots = -b/a ⇒ p + q = - p .......(1) ⇒ Product of the roots = c/a ⇒ pq = q ⇒ pq - q = 0 ⇒ q (p - 1) = 0 ⇒ q = 0 or p = 1. Case-1: If q = 0, then p = 0. i.e. p = q = 0 (By substituting value of p in equation 1) Case-2: If p = 1, then q = -2 (By substituting value of p in equation 1)