The complete solution set of inequality (x−5)1005(x+8)1008(x−1)x1006(x−2)3(x−3)5(x−6)(x+9)1010≤0 is

We have (x−5)1005(x+8)1008(x−1)x1006(x−2)3(x−3)5(x−6)(x+9)1010≤0From the sign schemex∈(−∞,9)∪(−9,0)∪(0,1]∪(2,3)∪[5,6)

The complete solution set of inequality (x−5)1005(x+8)1008(x−1)x1006(x−2)3(x−3)5(x−6)(x+9)1010≤0 is

We have (x−5)1005(x+8)1008(x−1)x1006(x−2)3(x−3)5(x−6)(x+9)1010≤0From the sign schemex∈(−∞,9)∪(−9,0)∪(0,1]∪(2,3)∪[5,6)

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The complete solution set of inequality $\frac{(x - 5)^{1005} (x + 8)^{1008} (x - 1)}{x^{1006} (x - 2)^{3} (x - 3)^{5} (x - 6) (x + 9)^{1010}} \leq 0$ is

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$(- \infty, - 9) \cup (- 8, 0) \cup (0, 1) \cup (2, 3) \cup [5, 6)$

$(- \infty, - 9) \cup (- 9, 0) \cup (0, 1) \cup (2, 3) \cup (5, 6)$

$(- \infty, - 9) \cup (- 9, 0) \cup (0, 1] \cup (2, 3) \cup [5, 6)$

$(- \infty, 0) \cup (0, 1] \cup (2, 3) \cup [5, 6)]$

answer is C.

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Detailed Solution

We have $\frac{(x - 5)^{1005} (x + 8)^{1008} (x - 1)}{x^{1006} (x - 2)^{3} (x - 3)^{5} (x - 6) (x + 9)^{1010}} \leq 0$

From the sign scheme

$x \in (- \infty, 9) \cup (- 9, 0) \cup (0, 1] \cup (2, 3) \cup [5, 6)$

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The complete solution set of inequality (x−5)1005(x+8)1008(x−1)x1006(x−2)3(x−3)5(x−6)(x+9)1010≤0 is

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The complete solution set of inequality $\frac{(x - 5)^{1005} (x + 8)^{1008} (x - 1)}{x^{1006} (x - 2)^{3} (x - 3)^{5} (x - 6) (x + 9)^{1010}} \leq 0$ is