Question

The range of values of ${}^{\prime }{x}^{\prime }$ which satisfies the inequation $\frac{(2x-1){(x-1)}^4{(x-2)}^4}{(x-2){(x-4)}^4}\le 0$ is

• A. $[\frac{1}{2},2)$
• B. R
• C. $\varphi$
• D. $(\frac{1}{2},2)$

Answer 1

The correct option is A $[\frac{1}{2},2)$

$\frac{(2x-1)(x-1{)}^4(x-2{)}^4}{(x-2)(x-4{)}^4}\le 0$

the critical points for number line method are $\Rightarrow x=\frac{1}{2},1,2,4$

$x\ne 2,x\ne 4$ as $(x-2)$ and $(x-4)$ are in denominator $\Rightarrow$

$\frac{(2x-1)(x-1)(x-2{)}^3}{(x-4{)}^4}\le 0$