If $\alpha,\ \beta$ are the roots of $\begin{vmatrix} x & 1 & 2\\ 0 & 1& 1\\ 1 & x & 2 \end{vmatrix}$ = 0 then $\alpha^{n}+\beta^{n}=?$

lf the lines $3\mathrm{x}+2\mathrm{y}-5=0,\ 2\mathrm{x}-5\mathrm{y}+3=0,\ 5\mathrm{x}+\mathrm{b}\mathrm{y}+\mathrm{c}=0$ are concurrent then $\mathrm{b}+\mathrm{c}=$

$A=\left[\begin{array}{ccc}a^{2} & b c & c a+c^{2} \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right]$ একটি নির্ণায়ক এবং $g(x)=x^{2}+3 x$.

The value of $\displaystyle \left | \begin{matrix} 11 & 12 & 13 \\ 12&13&14 \\ 13&14&15 \end{matrix} \right |$ is,

Find the values of $k,$ if the points $A (k + 1, 2k), B (3k, 2k + 3)$ and $C (5k +1, 5k)$ are collinear.