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If one of the roots of $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ is -10 , then the other roots are
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The correct answer is:
3, 7
Given, $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$
$\begin{array}{cc}
\Rightarrow & 3(3 x-35)-5(21-7 x)+x\left(35-x^2\right)=0 \\
\Rightarrow & 9 x-105-105+35 x+35 x-x^3=0 \\
\Rightarrow & x^3-79 x+210=0 \\
\Rightarrow & (x+10)(x-3)(x-7)=0 \\
\Rightarrow & x=-10,3,7
\end{array}$
$\begin{array}{cc}
\Rightarrow & 3(3 x-35)-5(21-7 x)+x\left(35-x^2\right)=0 \\
\Rightarrow & 9 x-105-105+35 x+35 x-x^3=0 \\
\Rightarrow & x^3-79 x+210=0 \\
\Rightarrow & (x+10)(x-3)(x-7)=0 \\
\Rightarrow & x=-10,3,7
\end{array}$
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