If $f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{5} & x^{2} & 1 1 & x^{3} - 1 & 1 + x + x^{2} 2 & x^{2} - 2 x + 1 & (1 - x)^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ is a polynomial of degree ‘n’. The coefficient of $x^{n}$ is A and constant term in the polynomial is B. Find the value of (n + A+ 2B)

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Solution

The correct option is C 17
Clearly highest power of ‘n’ is ‘10’ and coefficient is ‘1’ and B = f(0).
$\Rightarrow B = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 0 & 1 1 & - 1 & 1 2 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ S o, n + A + 2 B = 10 + 1 + 6 = 17$

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