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(A) Given the determinant equation: $\left| \begin{array}{ccc} x & 3 & 7 \ 2 & x & 2 \ 7 & 6 & x \end{array} ight| = 0$. Applying the row operatio

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$2, 7$

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(A) Given the determinant equation: $\left| \begin{array}{ccc} x & 3 & 7 \ 2 & x & 2 \ 7 & 6 & x \end{array} ight| = 0$. Applying the row operation $R_1 	o R_1 + R_2 + R_3$,we get: $\left| \begin{array}{ccc} x+9 & x+9 & x+9 \ 2 & x & 2 \ 7 & 6 & x \end{array} ight| = 0$. Taking $(x+9)$ as a common factor from $R_1$: $(x+9) \left| \begin{array}{ccc} 1 & 1 & 1 \ 2 & x & 2 \ 7 & 6 & x \end{array} ight| = 0$. Expanding the determinant: $(x+9) [1(x^2 - 12) - 1(2x - 14) + 1(12 - 7x)] = 0$. $(x+9) [x^2 - 12 - 2x + 14 + 12 - 7x] = 0$. $(x+9) (x^2 - 9x + 14) = 0$. Factoring the quadratic expression: $(x+9) (x-2) (x-7) = 0$. Thus,the roots are $x = -9, 2, 7$. The other two roots are $2$ and $7$.

If $-9$ is a root of the equation $\left| \begin{array}{ccc} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{array} \right| = 0$,then the other two roots are:

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