= Solution
A positive-radius horizon occurs at a zero of V. Set $u=r^2>0$; multiplying by $r^4$ gives $u^2-2Mu+Q^2=0$. Thus real roots require $M^2-Q^2\geq0$. With $M>0$, the horizon condition and radii are
$$
\boxed{|Q|\leq M,\qquad r_\pm^2=M\pm\sqrt{M^2-Q^2}.}
$$
For $0<|Q|<M$ both roots are positive, giving an outer <event horizon> and an inner <Cauchy horizon>. For $|Q|=M$ they coincide at $r_h=\sqrt M$. For $Q=0$ only $r_+=\sqrt{2M}$ is a horizon: the formal root $u=0$ was introduced by multiplication and is the singular origin, where the original expression for V is undefined. For $|Q|>M$ there is no horizon and the central singularity is naked. Each positive root is regular in ingoing coordinates $v=t+r_*$, where the radial metric is $-Vdv^2+2dv\,dr$.
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