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Matrices and Determinants question

2005 · Shift 0 · Q77

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JEE Main
Mathematics
Matrices and Determinants
2005 · Shift 0 · Q77

Matrices and Determinants question

2005 · Shift 0 · Q77

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

{a^2} + {b^2} + {c^2} = - 2

and f

\left( x \right) = \left| {\begin{matrix} {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \\ {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \\ {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \\ \end{matrix} } \right|,

then f

(x)

is a polynomial of degree :

A
$1$
B
$0$
C
$3$
D
$2$

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