Mathematics - Determinant Question with Solution | TestHub

$\Delta =\left|\begin{array}{ccc}x-2& 2x-3& 3x-4\\ 2x-3& 3x-4& 4x-5\\ 3x-5& 5x-8& 10x-17\end{array}\right|$

Applying $R_2\to R_2-R_1$, $R_3\to R_3-R_2$, we get

$\Delta =\left|\begin{array}{ccc}x-2& 2x-3& 3x-4\\ x-1& x-1& x-1\\ x-2& 2\left(x-2\right)& 6\left(x-2\right)\end{array}\right|=\left(x-1\right)\left(x-2\right)\left|\begin{array}{ccc}x-2& 2x-3& 3x-4\\ 1& 1& 1\\ 1& 2& 6\end{array}\right|$

$=-3x^3+12x^2-15x+6$

$\therefore B+C=12-15=-3$