Question

Find the integral value of $x$, if $\left|\begin{array}{ccc}{x}^2& x& 1\\ 0& 2& 1\\ 3& 1& 4\end{array}\right|=28$

Answer 1

$\left|\begin{array}{ccc}{x}^2& x& 1\\ 0& 2& 1\\ 3& 1& 4\end{array}\right|=28$

$x^2(8-1)-x(0-3)+1(0-6)=28$

$7x^2+3x-6=28$

$7x^2+3x-34=0$

$7x^2+17x-14x-34=0$

$(7x+17)(x-2)=0$

$x=2$ or $\frac{-17}{7}$

Since, x is an integer, $x=2$.