Let $ax^{6} + bx^{5} + cx^{4} + dx^{3} + ex^{2} + fx + g = \left| \begin{matrix} (x + 1) & (x^{2} + 2) & (x^{2} + x) \ (x^{2} + x) & (x^{2} + 1) & (x^{2} + 2) \ (x^{2} + 2) & (x^{2} + x) & (x + 1) \end{matrix} ight|.\$Then,

Question

Let $ax^{6} + bx^{5} + cx^{4} + dx^{3} + ex^{2} + fx + g = \left| \begin{matrix} (x + 1) & (x^{2} + 2) & (x^{2} + x) \ (x^{2} + x) & (x^{2} + 1) & (x^{2} + 2) \ (x^{2} + 2) & (x^{2} + x) & (x + 1) \end{matrix} ight|.\$Then,

Dr. Abubacker · Accepted Answer

(d)
On putting $x = 0$ in the given equation, we get
$g = \left| \begin{matrix}
1 & 2 & 0 \
0 & 1 & 2 \
2 & 0 & 1
\end{matrix} ight| = 9$
On differentiating given equation and then put $x = 0$, we get
$f = - 5$

Q. Let $ax^{6} + bx^{5} + cx^{4} + dx^{3} + ex^{2} + fx + g = \left| \begin{matrix} (x + 1) & (x^{2} + 2) & (x^{2} + x) \\ (x^{2} + x) & (x^{2} + 1) & (x^{2} + 2) \\ (x^{2} + 2) & (x^{2} + x) & (x + 1) \end{matrix} \right|.\$Then,

Explanation

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