Question

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

• A. $2$
• B. $0$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

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

$\Rightarrow \frac{3x-4}{2x-7}\le 0$ and $x=0,2,\ne 7/2$

$\Rightarrow \frac{4}{3}\le x<5$ and $x=0,2,\ne 7/2$

Hence, number of integral solution is $\{0,2,3,4\}=4$

And number of positive integral solution are $2,3,4$

Thus the number of integral solutions are $3$