Question

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

Answer 1

$\left|\begin{array}{ccc}1& 4& 20\\ 1& -2& 5\\ 1& 2x& 5x^2\end{array}\right|=0\Rightarrow 1(-10x^2-10x)-4(5x^2-5)+20(2x+2)=0\Rightarrow -30x^2+30x+60=0\Rightarrow (x-2)(x+1)=0\Rightarrow x=2,-1$
Hence the sum of solution is $2-1=1$