6. Given two quadratic equations
$$
a x^{2}+b x+c=0, u x^{2}+v x+w=0(a \neq u)
$$

both have real roots. If the coefficients of the quadratic terms of these two equations are swapped, then $w c>0$ is the ( ) condition for at least one of the two quadratic equations obtained after the swap to have real roots.
(A) Sufficient but not necessary
(B) Necessary but not sufficient
(C) Sufficient and necessary
(D) Neither sufficient nor necessary