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Question

If a2+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∣∣ ∣ ∣∣
then f(x) is a polynomial 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∣ ∣ ∣
Applying C1C1+C2+C3

f(x)=∣ ∣ ∣1+a2x+(1+b2)x+(1+c2)x(1+b2)x(1+c2)x(1+a2)x+(1+b2)x+(1+c2)x1+b2x(1+c2)x(1+a2)x+(1+b2)x+(1+c2)x(1+b2)x1+c2x∣ ∣ ∣

f(x)=(1+x(2+a2+b2+c2))∣ ∣ ∣1(1+b2)x(1+c2)x11+b2x(1+c2)x1(1+b2)x1+c2x∣ ∣ ∣
Applying R2R2R1,R3R3R1
f(x)=(1+x(22))∣ ∣ ∣1(1+b2)x(1+c2)x01x0001x∣ ∣ ∣f(x)=(1x)2

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