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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
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The roots of the equation $\begin{vmatrix}x-1&1&1\\1&x-1&1\\1&1&x-1\end{vmatrix}=0$ are

$\begin{array}{1 1}(A)\;1,2&(B)\;-1,2\\(C)\;1,-2&(D)\;-1,-2\end{array}$

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1 Answer

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Given :
Operating $C_1=C_1+C_2+C_3$
$\Rightarrow (x+1)\begin{vmatrix}1& 1&1\\1&x-1&1\\1&1&x-1\end{vmatrix}=0$
Apply $R_2-R_1$ and $R_3-R_1$ and get
$\Rightarrow (x+1)(x-2)^2=0$
Hence (B) is the correct answer.
answered Apr 23, 2014 by sreemathi.v

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