= Random quadratic with uniform coefficients
{title2=$r^2+2Vr+U=0$}
For independent $U,V$ uniform on $[0,1]$, real roots occur on $U\leq V^2$, a region of <probability> $1/3$. On that region both roots are nonpositive. Both lie in $[-1,0]$ exactly when $\max(0,2V-1)\leq U\leq V^2$. Its area is $1/12$, so the conditional <probability> of both absolute values being at most one is $1/4$. <Joint probability density> integration turns algebraic <discriminant> and root constraints into simple planar areas.
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