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Question: Let ax<sup>7</sup> + bx<sup>6</sup> + cx<sup>5</sup> + dx<sup>4</sup> + ex<sup>3</sup> + fx<sup>2</s...

Let ax7 + bx6 + cx5 + dx4 + ex3 + fx2 + gx + h =

∣(x+1)(x2+2)(x2+x)(x2+x)(x+1)(x2+2)(x2+2)(x2+x)x+1∣\left| \begin{matrix} (x + 1) & (x^{2} + 2) & (x^{2} + x) \\ (x^{2} + x) & (x + 1) & (x^{2} + 2) \\ (x^{2} + 2) & (x^{2} + x) & x + 1 \end{matrix} \right|. Then

A

g = 3 and h = – 5

B

g = –3 and h = – 5

C

g = –3 and h = –9

D

None of these

Answer

None of these

Explanation

Solution

By putting x = 0 on both sides of the equation we have =∣⥄⥄120012201⥄⥄∣= \left| ⥄ ⥄ \begin{matrix} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1 \end{matrix} ⥄ ⥄ \right|= 9