The sum of solutions of the equation $\left|\begin{array}{ccc}1 & 4 & 20 \ 1 & -2 & 5 \ 1 & 2 x &

Question

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

Professor PC Thomas Classes · Answer

Expanding, $1\left(-10 x^{2}-10 xight) -4\left(5 x^{2}-5ight)+20(2 x+2)=0 $ \ $\Rightarrow \quad-30 x^{2}+30 x+60=0$\ $\Rightarrow x^{2}-x-2=0 \Rightarrow(x-2)(x+1)=0$\ $\Rightarrow \quad x=2,-1$\ Hence the solution set is $\{2,-1\}$\