Question

The equation $\Delta =\left|\begin{array}{ccc}x-a& x-b& x-c\\ x-b& x-c& x-a\\ x-c& x-a& x-b\end{array}\right|=0$ 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 $C_1\to C_1+C_2+C_3$, we get
$\Delta =\left|\begin{array}{ccc}3x-(a+b+c)& x-b& x-c\\ 3x-(a+b+c)& x-c& x-a\\ 3x-(a+b+c)& x-a& x-b\end{array}\right|$
Note that $\Delta$ becomes 0 when $x=\frac{1}{3}(a+b+c)$.