If $A=\left[\begin{array}{lll}2 & 3 & 4 \ 1 & k & 2 \ 4 & 1 & 5\end{array} ight]$ is singular matrix, then the quadratic equation having the roots $k$ and $\frac{1}{k}$ is

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If $A=\left[\begin{array}{lll}2 & 3 & 4 \ 1 & k & 2 \ 4 & 1 & 5\end{array}ight]$ is singular matrix, then the quadratic equation having the roots $k$ and $\frac{1}{k}$ is

Aicharya · Accepted Answer

$\left|\begin{array}{lll}2 & 3 & 4 \ 1 & k & 2 \ 4 & 1 & 5\end{array}ight|=0$ $\begin{aligned} & \Rightarrow 2(5 k-2)-3 	imes(-3)+4(1-4 k)=0 \ & \Rightarrow k=\frac{3}{2} \end{aligned}$ Required quadratic equation $\begin{aligned} & \left(x-\frac{3}{2}ight)\left(x-\frac{2}{3}ight)=0 \ & x^2-\frac{13}{6} x+1=0 \Rightarrow 6 x^2-13 x+6=0 \end{aligned}$

If $A=\left[\begin{array}{lll}2 & 3 & 4 \\ 1 & k & 2 \\ 4 & 1 & 5\end{array}\right]$ is singular matrix,…

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