Question

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

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

Answer 1

Answer: (B)

Given $\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0$
Operate $R_2\to R_2-R_1$ and $R_3\to R_3-R_1$
Thus we get: $\left|\begin{array}{ccc}1& 4& 20\\ 0& -6& -15\\ 0& 2x-4& 5x^2-20\end{array}\right|=0$
$\Rightarrow 1[-30x^2+120+30x-60]=0$
$\Rightarrow 30x^2-30x-60=0$
$\Rightarrow x=-1,2.$
$\therefore$ roots are - 1 and 2