Matrices and Determinants 2 Question 27
30. The solution set of the equation $\begin{vmatrix}1 & 4 & 20 \\ 1 & -2 & 5\end{vmatrix}=0$ is…
(1981, 2M)
Show Answer
Answer:
Correct Answer: 30. (-1 ,2)
Solution:
- Given, $\begin{vmatrix}1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & 2 x & 5 x^{2}\end{vmatrix}=0$
$\Rightarrow 1\left(-10 x^{2}-10 x\right)-4\left(5 x^{2}-5\right)+20(2 x+2)=0 $
$\Rightarrow -30 x^{2}+30 x+60=0 $
$\Rightarrow (x-2)(x+1)=0 $
$\Rightarrow x=2,-1$
Hence, the solution set is ${-1,2}$.
