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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 6 · Set 3 · Q26
Find the value of x, if [1, x, 1] [1, 3, 2; 2, 5, 1; 15, 3, 2] [1; 2; x] = O.
Find the value of x , if $\displaystyle \left[\begin{array}{lll}1 & \mathrm{x} & 1\end{array}\right]\left[\begin{array}{ccc}1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2\end{array}\right]\left[\begin{array}{l}1 \\ 2 \\ \mathrm{x}\end{array}\right]=\mathrm{O}$.
Marking-scheme solution
\[\begin{gathered}
{\left[\begin{array}{lll}
1 & \mathrm{x} & 1
\end{array}\right]\left[\begin{array}{ccc}
1 & 3 & 2 \\
2 & 5 & 1 \\
15 & 3 & 2
\end{array}\right]\left[\begin{array}{l}
1 \\
2 \\
\mathrm{x}
\end{array}\right]=0} \\
{\left[\begin{array}{lll}
1 & \mathrm{x} & 1
\end{array}\right]\left[\begin{array}{c}
7+2 \mathrm{x} \\
12+\mathrm{x} \\
21+2 \mathrm{x}
\end{array}\right]=0} \\
\mathrm{x}^{2}+16 \mathrm{x}+28=0 \\
\Rightarrow(\mathrm{x}+14)(\mathrm{x}+2)=0 \\
\Rightarrow \mathrm{x}=-14, \mathrm{x}=-2
\end{gathered}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.