Question

$\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$ find x

• A. -1, 2
• B. 0,1
• C. 1, 3
• D. 2, 0

Answer 1

The correct option is A -1, 2

$\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$
$r_1\to r_1-r_2$ and $r_3\to r_3-r_2$
$\left|\begin{array}{ccc}0& 6& 15\\ 1& -2& 5\\ 0& 2x+2& 5x^2-5\end{array}\right|$
$=-\left(6\right(5x^2-5)-15(2x+2\left)\right)$
$=-(30x^2-30-30x-30)$
$=30(-x^2+x+2)$
So, $x^2-x-2=0$
$x=-1,2$