Question

The roots of the determinantal equation $\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|$ =0 are

• A. $a$
• B. $b$
• C. $a$ or $b$
• D. $0,0$

Answer 1

Answer: (C)

$a$ or $b$

Given, $\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& n\end{array}\right|=0$

by $C_1\to C_1-C_2$ and $C_3\to C_3-C_2$

So,$\left|\begin{array}{ccc}0& a& x-a\\ 0& m& 0\\ b-x& x& b-x\end{array}\right|(b-x)[-m(x-a\left)\right]=0$

$x=a,b$ are two solution