Question

If $S$ is the set of all real values of $x$ such that $\frac{2x-1}{2x^3+3x^2+x}$ is positive, then $S$ contains

• A. $(-\infty ,-\frac{3}{2})$
• B. $(-\frac{1}{2},0)$
• C. $(\frac{1}{2},3)$
• D. $(-\frac{1}{2},\frac{1}{2})$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $(-\infty ,-\frac{3}{2})$
B $(-\frac{1}{2},0)$
C $(\frac{1}{2},3)$

$\frac{2x-1}{2x^3+3x^2+x}>0\Rightarrow \frac{2x-1}{x(x+1)(2x+1)}>0$


$\therefore x\in (-\infty ,-1)\cup (-\frac{1}{2},0)\cup (\frac{1}{2},\infty )=S$
$\therefore S$ contains option $a,b,c$ but not $d$