The roots of the equation $\left| {\,\begin{array}{*{20}{c}}x&0&8\\4&1&3\\2&0&x\end{array}\,} \right| = 0$ are equal to

If $\left| \begin{array}{*{20}{c}}
{ – 2a}&{a + b}&{a + c}\\
{b + a}&{ – 2b}&{b + c}\\
{c + a}&{b + c}&{ – 2c}
\end{array}\right|$ $ = \alpha \left( {a + b} \right)\left( {b + c} \right)\left( {c + a} \right) \ne 0$ then $\alpha $ is equal to

If $ 5$  is one root of the equation $\left| {\,\begin{array}{*{20}{c}}x&3&7\\2&x&{ – 2}\\7&8&x\end{array}\,} \right| = 0$, then other two roots of the equation are

If the system of linear equations $x+y+3 z=0$

$x+3 y+k^{2} z=0$

$3 x+y+3 z=0$

has a non-zero solution $(x, y, z)$ for some $k \in R ,$ then $x +\left(\frac{ y }{ z }\right)$ is equal to

$\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{m{a_1}}&{{b_1}}\\{{a_2}}&{m{a_2}}&{{b_2}}\\{{a_3}}&{m{a_3}}&{{b_3}}\end{array}\,} \right| = $