Question

Solve: $\left|\begin{array}{ccc}3x+4& x+2& 2x+3\\ 4x+5& 2x+3& 3x+4\\ 10x+17& 3x+5& 5x+8\end{array}\right|=0$. The value of the determinant at $x=-1$is:

Answer 1

$\left|\begin{array}{ccc}3x+4& x+2& 2x+3\\ 4x+5& 2x+3& 3x+4\\ 10x+17& 3x+5& 5x+8\end{array}\right|=0$

at $x=-1\left|\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 7& 2& 3\end{array}\right|$

$R_2\to R_2-R_1=\left|\begin{array}{ccc}1& 1& 1\\ 0& 0& 0\\ 7& 2& 3\end{array}\right|$

So,determinant is $0$