Testing the Cubic Solution

$(x-\lambda_1)(x-\lambda_2)(x-\lambda_3) = ax^3+bx^2+cx+d$, with $a=1$, $b=-\lambda_1-\lambda_2-\lambda_3$, $c=\lambda_1\lambda_2+\lambda_1\lambda_3+\lambda_2\lambda_3$ and $d=\lambda_1\lambda_2\lambda_3$.

Note. A swap-dance for $\lambda_2$ and $\lambda_3$ becomes a return-dance of a,b,c,d, yet a one-way dance for $r$.