QJEEM11Ma111f: JEE Main 2011 Mathematics - Class 12 JEEM11Ma111f Solution: The number of values of k for which the linear equations 4 x +…

Question

Verified Solution • 2025–26 Session moderate

The number of values of

k

for which the linear equations

4 x + k y + 2 z = 0, k x + 4 y + z = 0

and

2 x + 2 y + z = 0

possess a non-zero solution is :

Accepted Answer

Δ = 0 \Rightarrow | \begin{matrix} 4 & k & 2 \\ k & 4 & 1 \\ 2 & 2 & 1 \end{matrix} | = 0

\Rightarrow 4 (4 - 2) - k (k - 2) +

2 (2 k - 8) = 0

\Rightarrow 8 - k^{2} + 2 k + 4 k - 16 = 0

\Rightarrow k^{2} - 6 k + 8 = 0

\Rightarrow (k - 4) (k - 2) = 0, k = 4, 2

Step-by-Step Verified Solution