JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For \(\alpha, \beta \in R\), suppose the system of linear equations \(x-y+z=5\) ; \( 2 x+2 y+\alpha z=8 \) ; \(3 x-y+4 z=\beta\) has infinitely many solutions. Then \(\alpha\) and \(\beta\) are the roots of
- A \(x ^2-10 x +16=0\)
- B \(x^2+18 x+56=0\)
- C \(x^2-18 x+56=0\)
- D \(x^2+14 x+24=0\)
Answer & Solution
Correct Answer
(C) \(x^2-18 x+56=0\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}\left|\begin{array}{ccc}1 & -1 & 1 \\ 2 & 2 & \alpha \\ 3 & -1 & 4\end{array}\right|=0 ; 8+\alpha-2(-4+1)+3(-\alpha-2)=0 \\ 8+\alpha+6-3 \alpha-6=0 \\ \alpha=4\end{array}\)
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