Mathematics · 2019
JEE Main · 10 April 2019, Shift 2 · Q65
Let λ be a real number for which the system of linear equations x+y+z=6; 4 x+λ y-λ z=λ-2; 3 x+2 y-4 z=-5 has infinitely many solutions. Then λ is a…
Let $\displaystyle \lambda$ be a real number for which the system of linear equations
$$\begin{aligned}
& x+y+z=6 \\
& 4 x+\lambda y-\lambda z=\lambda-2 \\
& 3 x+2 y-4 z=-5
\end{aligned}
$$
has infinitely many solutions. Then $\displaystyle \lambda$ is a root of the quadratic equation :
Official answer
(4)
$\displaystyle \lambda^2-\lambda-6=0$
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JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.