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Question

If a2+b2+c2+2=0 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∣∣ ∣ ∣∣ then f(x) is poynomial of degree

A
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B
1
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C
2
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D
3
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Solution

The correct option is C 2
f(x)=∣ ∣ ∣1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x∣ ∣ ∣
R1R1R2,R2R2R3
=∣ ∣ ∣1xx1001xx1(1+a2)x(1+b2)x1+c2x∣ ∣ ∣
f(x)=(x1)2∣ ∣ ∣110011(1+a2)x(1+b2)x1+c2x∣ ∣ ∣
C1C1+C2+C3
f(x)=(x1)2∣ ∣ ∣0100111+(a2+b2+c2+2)x(1+b2)x1+c2x∣ ∣ ∣
f(x)=(1+(a2+b2+c2+2)x)(x1)2
f(x)=(x1)2
Hence, f(x) is a polynomial of degree 2

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