Question

Find the value of $x$ in the equation $\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$

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

Answer 1

The correct option is A $-1,2$

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

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

$\Rightarrow \left|\begin{array}{ccc}1& 4& 20\\ 0& -6& -15\\ 0& 2x-4& 5x^2-20\end{array}\right|=0$

$\Rightarrow -6(5x^2-20)+15(2x-4)=0$

$\Rightarrow -30x^2+120+30x-60=0$

$\Rightarrow 30x^2-30x-60=0$

$\Rightarrow x^2-x-2=0$

$\Rightarrow (x-2)(x+1)=0$

$\Rightarrow x=-1,2$