If $a,b,c$ are the roots of $ x^3+x^2-2x+1=0$, then what is the value of $\det\Delta$ where:
$$\Delta=\begin{bmatrix} c^2 & b^2 & 2bc-a^2 \\ 2ac-b^2 & a^2 & c^2 \\ a^2 & 2ab-c^2 & b^2 \\ \end{bmatrix}$$
The roots are not simply resolvable. So my experience tells me that we need to convert $\Delta$ into a form that contains $a+b+c$ or $ab+bc+ca$ or $abc$.
Since expanding this determinant would be tedious, please suggest a method that doesn't require it.
All help will be appreciated
Hint: For your determinant we get $$ \left( b+a+c \right) ^{2} \left( {b}^{2}-ab-bc-ac+{a}^{2}+{c}^{2} \right) ^{2} $$