Question

The solution set of the equation
$\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$ is

• A. {0, 1}
• B. {1, 2}
• C. {1, 5}
• D. {2, - 1}

Answer 1

Answer: (D)

Given $\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$
Operate, $R_2\to R_2-R_1{R}_3\to R_3-R_1$
$\left|\begin{array}{ccc}1& 4& 20\\ 0& -6& -15\\ 0& 2x-4& 5x^2-20\end{array}\right|=0$
$\Rightarrow 1\left[-30x^2+120+30x-60\right]=0$
$\Rightarrow 30x^2-30x-60=0$
$\Rightarrow x^2-x-2=0$
$\Rightarrow \left(x-2\right)\left(x+1\right)=0$
$\Rightarrow x=-1,2$
Thus, solution set is {2, - 1}.