- (B) Work done by gravity is negative because the gravitational force opposes the upward motion.
- (E) Work done by air resistance is always negative because it opposes motion.
- Other statements are incorrect because:
- (A) Work done by a man is positive as the applied force is in the direction of displacement.
- (C) Work done by friction is negative, not positive.
- (D) Work done is zero only if there is no displacement, not due to roughness.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
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