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The equation $6 x^{6} - 25 x^{5} + 31 x^{4} - 31 x^{2} + 25 x - 6 = 0$ is reciprocal equation of

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class two and x = ±1 are roots

class one and x =1 is a root

class two and x = 1 is a root but not x = –1

class one and x = –1 is a root

answer is C.

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Detailed Solution

$\begin{array}{l} G i v e n 6 x^{6} - 25 x^{5} + 31 x^{4} - 31 x^{2} + 25 x - 6 = 0 \\ p (x) = - x^{n} p (\frac{1}{x}) \\ T h e E q u a t i o n i s Re c i p r o c a l E q u a t i o n o f c l a s s' 2' \\ ∴ x = \pm 1 a r e r o o t s \end{array}$

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