Let \( \left|\begin{array}{ccc}1+x & x & x^{2} \\ x & 1+x & x^{2} \\ x^{2} & x & 1+x\end{array}\... VIDEO
Let \( \left|\begin{array}{ccc}1+x & x & x^{2} \\ x & 1+x & x^{2} \\ x^{2} & x & 1+x\end{array}\right|=a x^{5}+b x^{4}+c x^{3}+d x^{2}+\lambda x+\mu \)
be an identity in \( x \), where \( a, b, c, d, \lambda, \mu \) are independent of \( x \). Then the value of \( \lambda \) is
(a) 3
(b) 2
(c) 4
(d) none of these
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