Question

The number of values of k for which the linear equations $4x + ky + 2z = 0$ , $kx + 4y + z = 0$ and $2x + 2y + z = 0$ possess a non-zero solution is

• A. 2
• B. 1
• C. 5
• D. 3

Answer 1

Answer: (A)

$\Delta = 0$
$ \Rightarrow \begin{vmatrix}4&k&2\\ k&4&1\\ 2&2&1\end{vmatrix} = 0 $
$\Rightarrow \ 4(4 - 2) - k(k - 2) + 2(2k - 8) = 0 $
$\Rightarrow \ 8 - k^2 + 2k + 4k - 16 = 0 $
$k^2 - 6k + 8 = 0 $
$\Rightarrow \ (k - 4 )(k-2) = 0 \ \Rightarrow \ k = 4 , 2 $