Question

If the polynomial \(f(x)=\left|\begin{array}{ccc}(1+x)^{a} & (2+x)^{b} & 1 \\ 1 & (1+x)^{a} & (2+x)^{b} \\ (2+x)^{b} & 1 & (1+x)^{a}\end{array}\right|\), then the constant term of \(f(x)\) is
(A) \(2-3.2^{\mathrm{b}}+2^{3 \mathrm{~b}}\)
(B) \(2+3.2^{b}+2^{3 b}\)
(C) \(2+3.2^{\mathrm{b}}-2^{3 \mathrm{~b}}\)
(D) \(2-3.2^{\mathrm{b}}-2^{3 \mathrm{~b}}\)

Answer 1

Ans: (A)
Hint \(: f(0)=\left|\begin{array}{rrr}1 & 2^{b} & 1 \\ 1 & 1 & 2^{b} \\ 2^{b} & 1 & 1\end{array}\right|=2-3.2^{b}+2^{3 b}\)

Answer 2

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Answer 3

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