The roots of $48 x^{3} - 44 x^{2} + 12 x - 1 = 0$ are in

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answer is C.

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Detailed Solution

$\begin{array}{l} G i v e n 48 x^{3} - 44 x^{2} + 12 x - 1 = 0 \\ L e t a = 48, b = - 44, c = 12, d = - 1 \\ I f r o o t s a r e i n A . P . t h e n a b^{3} + 27 a^{2} d = 9 a b c \\ 48 {(- 44)}^{3} + 27 {(48)}^{2} (- 1) \neq 9 (48) (- 44) (12) \\ I f r o o t s a r e i n G . P t h e n a c^{3} = b^{3} d \\ \Rightarrow 48 {(12)}^{3} \neq {(- 44)}^{3} (- 1) \\ I f t h e r o o t s a r e i n H . P t h e n \\ 2 c^{3} + 27 a d^{2} = 9 b c d \\ \Rightarrow 2 {(12)}^{3} + 27 (48) {(- 1)}^{2} = 9 (- 44) (12) (- 1) \\ \Rightarrow 4752 = 4752 \\ ∴ r o o t s a r e i n H . P \end{array}$