Q. If $a \neq b \neq c$, the value of $x$ which satisfies the equation $\left| \begin{matrix} 0 & x - a & x - b \\ x + a & 0 & x - c \\ x + b & x + c & 0 \end{matrix} \right| = 0,$ is
A) $x = 0$
B) $x = a$
C) $x = b$
D) $x = c$
Explanation
(a)
On putting $x = 0,$we observe that the determinant becomes zero.
$\therefore\mathrm{\Delta} = \left| \begin{array}{r}
0\ –a\ - b \\
a\ \ \ \ 0\ - c \\
b\ \ \ \ \ c\ \ \ \ \ \ 0
\end{array} \right|$
$= a(bc) - b(ac) = 0$
Hence, $x = 0$ is a root of the given equation
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.