If `a ,\ b ,\ c` are roots of the equation `x^3+p x^{2}+q=0` , prove that `|a b c b c a c a b|=a^3` .

Explanation

$$
\begin{aligned}
&=\left|\begin{array}{ccc}
a & a+b & a+b+c \\
2 a & 3 a+2 b & 4 a+3 b+2 c \\
3 a & 6 a+3 b & 10 a+6 b+3 c
\end{array}\right| \\
&=\left|\begin{array}{ccc}
...