If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x\\ \end{matrix} \right|\] then f(x) is a polynomial of degree [AIEEE 2005]

If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left| \begin{matrix

1.	If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left\| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x\\ \end{matrix} \right\|\] then f(x) is a polynomial of degree [AIEEE 2005]
A.	3
B.	2
C.	1
D.	0
Answer» C. 1

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If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2\]and \[f(x)=\left| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x\\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x\\ \end{matrix} \right|\] then f(x) is a polynomial of degree [AIEEE 2005]

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