The number of positive integral solutions of x23 x-43x-24-x-552 x-76- 0 isA- ThreeB- FourC- TwoD- Only one

The correct option is A Three Since, x^2(3x 4)^3 (x 2)^4/(x 5)^5 (2x 7)^6≤ 0 ∴ x ϵ [ 4/3, 7/2 ) ∪ ( 7/2, 5 ) ∴ x = 2, 3, 4 ...

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Standard XII

Mathematics

Nature of Roots

The number of...

Question

The number of positive integral solutions of $\frac{x^{2} (3 x - 4)^{3} (x - 2)^{4}}{(x - 5)^{5} (2 x - 7)^{6}} \leq 0$ is

Four

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Three

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Two

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Only one

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Solution

The correct option is B
Three

Since, $\frac{x^{2} (3 x - 4)^{3} (x - 2)^{4}}{(x - 5)^{5} (2 x - 7)^{6}} \leq 0$

$∴ x ϵ [\frac{4}{3}, \frac{7}{2}) \cup (\frac{7}{2}, 5)$

$∴ x = 2, 3, 4$

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The number of positive integral solutions of x2(3x−4)3(x−2)4(x−5)5(2x−7)6≤0 is

The correct option is B Three Since, x2(3x−4)3(x−2)4(x−5)5(2x−7)6≤0 ∴xϵ[43,72)∪(72,5) ∴x=2,3,4

The number of positive integral solutions of $\frac{x^{2} (3 x - 4)^{3} (x - 2)^{4}}{(x - 5)^{5} (2 x - 7)^{6}} \leq 0$ is

The correct option is B
Three

Since, $\frac{x^{2} (3 x - 4)^{3} (x - 2)^{4}}{(x - 5)^{5} (2 x - 7)^{6}} \leq 0$

$∴ x ϵ [\frac{4}{3}, \frac{7}{2}) \cup (\frac{7}{2}, 5)$

$∴ x = 2, 3, 4$