Q. The solutions of the equation$\left| \begin{matrix} x & 2 & - 1 \\ 2 & 5 & x \\ - 1 & 2 & x \end{matrix} \right| = 0,\$are
A) 3, $- 1$
B) $- 3,\ 1$
C) 3, 1
D) $- 3, - 1$
Explanation
(a)
Given$\left| \begin{matrix}
x & 2 & - 1 \\
2 & 5 & x \\
- 1 & 2 & x
\end{matrix} \right| = 0$
$\Rightarrow \left| \begin{matrix}
x & 2 & - 1 \\
2 & 5 & x \\
- 3 & - 3 & 0
\end{matrix} \right| = 0$ $\lbrack R_{3} \rightarrow R_{3} - R_{2}\rbrack$
$\Rightarrow - 1( - 6 + 15) - x\lbrack - 3x + 6\rbrack = 0$
$\Rightarrow \ \ \ x^{2} - 2x - 3 = 0$
$\Rightarrow x = 3, - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.