The roots of the equation left| begin{matrix} | vedclass

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(B) Given the determinant equation: $\left| \begin{matrix} 1+x & 1 & 1 \ 1 & 1+x & 1 \ 1 & 1 & 1+x \end{matrix} ight| = 0$Apply the column operati

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$0, 0, -3$

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(B) Given the determinant equation: $\left| \begin{matrix} 1+x & 1 & 1 \ 1 & 1+x & 1 \ 1 & 1 & 1+x \end{matrix} ight| = 0$Apply the column operation $C_1 	o C_1 + C_2 + C_3$:$\left| \begin{matrix} 3+x & 1 & 1 \ 3+x & 1+x & 1 \ 3+x & 1 & 1+x \end{matrix} ight| = 0$Take $(x+3)$ common from $C_1$:$(x+3) \left| \begin{matrix} 1 & 1 & 1 \ 1 & 1+x & 1 \ 1 & 1 & 1+x \end{matrix} ight| = 0$Apply row operations $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$:$(x+3) \left| \begin{matrix} 1 & 1 & 1 \ 0 & x & 0 \ 0 & 0 & x \end{matrix} ight| = 0$Expanding along $C_1$,we get:$(x+3)(1)(x^2 - 0) = 0$$(x+3)x^2 = 0$Thus,the roots are $x = 0, 0, -3$.

The roots of the equation $\left| \begin{matrix} 1+x & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+x \end{matrix} \right| = 0$ are

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