Question

Number of positive integral solution of $\frac{x^3(2x-3{)}^2(x-4{)}^6}{(x-3{)}^3(3x-8{)}^4}\le 0$

• A. only one
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$x^3(2x-3{)}^2(x-4{)}^6=0$

$(x-3{)}^3(3x-8{)}^4$

$x=0,3/2,4,8/3$

$\therefore xϵ[0,3/2]\cup [3/2,8/3]\cup (8/3,3)\cup 4$

$\Rightarrow xϵ(0,8/3)\cup (8/3,3)\cup 4$

$\therefore$ positive integral solutions

$\Rightarrow x=1,2,4$