If $a,b,c$ are the roots of $x^3+x^2-2x+1=0$ then what is the value of $\det\Delta$? 
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 $$ \left( b+a+c \right) ^{2} \left( {b}^{2}-ab-bc-ac+{a}^{2}+{c}^{2}
 \right) ^{2}
$$
