Question

If $x=-1$ is a root of the equation $\left|\begin{array}{ccc}2-x& 3& 3\\ 3& 4-x& 5\\ 3& 5& 4-x\end{array}\right|=0$ then the other roots are

• A. 0,11
• B. 11,12
• C. 0, 12
• D. 1,11

Answer 1

Answer: (A)

0,11

$R_2\to R_2-R_3$

$\left|\begin{array}{ccc}2-x& 3& 3\\ 0& -1-x& 1+x\\ 3& 5& 4-x\end{array}\right|=0$

$C_2\to C_2+C_3$

$\left|\begin{array}{ccc}2-x& 6& 3\\ 0& 0& 1+x\\ 3& 9-x& 4-x\end{array}\right|=0$

$-(x+1)\left\{\right(x-2\left)\right(x-9)-18\}=0$
$-(x+1)(x^2-11x)=0$
$-x(x+1)(x-11)=0$
other roots $x=0and11$