Matrices and Determinants 2 Question 27
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30. The solution set of the equation $\begin{array}{cccc}1 & 4 & 20 \ 1 & -2 & 5\end{array}=0$ is… . $12 x \quad 5 x^{2}$
======= ####30. The solution set of the equation $\begin{vmatrix}1 & 4 & 20 \\ 1 & -2 & 5\end{vmatrix}=0$ is…
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed
(1981, 2M)
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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 ${-1,2}$.
