JEE Main 2005Annual, Paper 1MathematicsHardMatrices and Determinants245× since 2002If a2+b2+c2=−2{a^2} + {b^2} + {c^2} = - 2a2+b2+c2=−2 and f(x)=∣1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x∣,\left( x \right) = \left| {\matrix{ {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \cr } } \right|,(x)=1+a2x(1+a2)x(1+a2)x(1+b2)x1+b2x(1+b2)x(1+c2)x(1+c2)x1+c2x, then f(x)(x)(x) is a polynomial of degree :AOption A. 111BOption B. 000COption C. 333DOption D. 222CheckSkip · show solution
