Question

The equation $\Delta=\begin{vmatrix} x-a & x-b & x-c \\ x-b & x-c & x-a \\ x-c & x-a & x-b \end{vmatrix}=0$ is satisfied when

• A. $x=\frac{1}{3}(a+b+c)$
• B. $x=\frac{1}{2}(a+b+c)$
• C. $x=a+b+c$
• D. $x=0$

Answer 1

Answer: (A)

Using $C_1 \rightarrow C_1+C_2+C_3$, we get
$\Delta=\begin{vmatrix}3 x-(a+b+c) & x-b & x-c \\3 x-(a+b+c) & x-c & x-a \\3 x-(a+b+c) & x-a & x-b\end{vmatrix}$
Note that $\Delta$ becomes 0 when $x=\frac{1}{3}(a+b+c)$.