Question

If $\left|\begin{array}{ccc}a& a& x\\ m& m& m\\ b& x& b\end{array}\right|=0$ then $x$ is:

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

Answer 1

Answer: (C)

$a$ or $b$

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

Expanding the determinant we get

$a(mb-mx)-a(mb-mb)+x(mx-mb)=0\Rightarrow a(mb-mx)-x(mb-mx)=0\Rightarrow (a-x)(mb-mx)=0\Rightarrow (a-x)(b-x)=0$

The solution for this quadratic equation is either $x=a$ or $x=b$