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

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Correct option is B

Applying , C1→C1+C2+C3 we get f(x)=11+b2x1+c2x11+b2x1+c2x11+b2x1+c2x [using a2+b2+c2=-2]Applying R2→R2-R1 and R3→R3-R1,we get f(x)=11+b2x1+c2x 01x0001-x =(1-x)2which is a polynomial of degree 2.

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If a2+b2+c2=-2 and f(x)=1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x then f(x) is a polynomial of degree

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