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$Number of positive integers satisfying \frac{(x + 2) (x^{2} - 2 x + 1)}{- 4 + 3 x - x^{2}} ≥ 0 is$

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Correct option is B

(x+2)x2−2x+1−x2+3x−4≥0⇒ (x+2)(x−1)2x2−3x+4≤0 but x2−3x+4>0∀x∈R since ∆ =9-4·1·4=-7<0 ∴ (x+2)(x−1)2≤0⇒ x∈(−∞,−2]∪{1} therefore only 1 is the positive integral solution

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Number of positive integers satisfying (x+2)x2−2x+1−4+3x−x2≥ 0 is

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$Number of positive integers satisfying \frac{(x + 2) (x^{2} - 2 x + 1)}{- 4 + 3 x - x^{2}} ≥ 0 is$