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. $\{-1,2\}$
• B. $\{1,2\}$
• C. $\{1,-2\}$
• D. None of the above

Answer 1

The correct option is D None of the above

The expansion of the determinant gives
$D=-30x-30+30x^2-30$
$=30x^2-30x+60$
$=0$
Hence, $x^2-x+2=0$
This equation has no real solutions.

So, option D is correct.