Question 323 of 472MediumMCQ
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 : Solutions · 1
Official solution
\[\Delta = 0 \Rightarrow \left| {4k2k42211 } \right| = 0\]
\[ \Rightarrow 4\left( {4 - 2} \right) - k\left( {k - 2} \right) + \]
\[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\left( {2k - 8} \right) = 0\]
\[ \Rightarrow 8 - {k^2} + 2k + 4k - 16 = 0\]
\[ \Rightarrow {k^2} - 6k + 8 = 0\]
\[ \Rightarrow \left( {k - 4} \right)\left( {k - 2} \right) = 0,k = 4,2\] Answer the question to unlock