If k_{i} are possible values of k for which l | vedclass

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(A) For three lines $a_1 x + b_1 y + c_1 = 0$,$a_2 x + b_2 y + c_2 = 0$,and $a_3 x + b_3 y + c_3 = 0$ to be concurrent,the determinant of their coeffi

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(A) For three lines $a_1 x + b_1 y + c_1 = 0$,$a_2 x + b_2 y + c_2 = 0$,and $a_3 x + b_3 y + c_3 = 0$ to be concurrent,the determinant of their coefficients must be zero:$\begin{vmatrix} k & 2 & 2 \ 2 & k & 3 \ 3 & 3 & k \end{vmatrix} = 0$Expanding the determinant:$k(k^2 - 9) - 2(2k - 9) + 2(6 - 3k) = 0$$k^3 - 9k - 4k + 18 + 12 - 6k = 0$$k^3 - 19k + 30 = 0$By testing roots,we find $(k - 2)$ is a factor:$(k - 2)(k^2 + 2k - 15) = 0$$(k - 2)(k + 5)(k - 3) = 0$The possible values are $k_1 = 2$,$k_2 = -5$,and $k_3 = 3$.The sum $\sum k_i = 2 + (-5) + 3 = 0$.

If $k_{i}$ are possible values of $k$ for which lines $kx + 2y + 2 = 0$,$2x + ky + 3 = 0$,and $3x + 3y + k = 0$ are concurrent,then $\sum k_{i}$ has the value

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