Question

If a + b + c = 0, then one root of $\left|\begin{array}{ccc}a-x& c& b\\ c& b-x& a\\ b& a& c-x\end{array}\right|$ =0 is

• A. a+b
• B. 0
• C. b+c
• D. a+c

Answer 1

Answer: (B)

0

Given $\left|\begin{array}{ccc}a-x& c& b\\ c& b-x& a\\ b& a& c-x\end{array}\right|=0$
and $a+b+c=0$
So, By column trasformation.
$C_1\to C_1+C_2+C_3$
$\left|\begin{array}{ccc}a+b+c-x& c& b\\ a+b+c-x& b-x& a\\ a+b+c-x& a& c-x\end{array}\right|=0$
$\Rightarrow (a+b+c-x)\left[\begin{array}{ccc}1& c& b\\ 1& b-x& a\\ 1& a& c-x\end{array}\right]=0$
So, $x\left[\begin{array}{ccc}1& c& b\\ 1& b-x& a\\ 1& a& c-x\end{array}\right]=0$
So, $x=0$