Question

Find x if it satisfies the equation$\left|\begin{array}{ccc}0& -3& x\\ x+1& 3& 1\\ 4& 1& 5\end{array}\right|=0$

Answer 1

$\therefore 0(15-1)+3(5x+5-4)+x(x+1-12)=0$
$\therefore 0+15x+3+x^2-11x=0$
$\therefore x^2+4x+3=0$
$\therefore (x+1)(x+3)=0$
$\therefore x+1=0$ or $x+3=0$
$\therefore x=-1$ or $x=-3$.