Q51 / 90 · JEE Main 2011 · Mathematics

The number of values of $\mathrm{k}$ for which the linear equations $4 x+k y+2 z=0 ; k x+4 y+z=0 ; 2 x+2 y+z=0$ possess a non-zero solution is

  • Correct answer
    A
    2
  • B
    1
  • C
    zero
  • D
    3

Solution

$\left|\begin{array}{lll}4 & k & 2 \\ k & 4 & 1 \\ 2 & 2 & 1\end{array}\right|=0 \Rightarrow k^2-6 k+8=0 \Rightarrow k=4,2$

Hence, the correct answer is option: 'A'.

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