Question

$m{x}^2+(m-1)x+2=0$ has roots on either side of x=1 the m $\in$

• A. $(\frac{-1}{2},0)$
• B. $(0,\frac{1}{2})$
• C. $(0,1)$
• D. None of these

Answer 1

The correct option is A $(\frac{-1}{2},0)$

$m{x}^2+(m-1)x+2=0$

Now, substituting $x=1$,

$\Rightarrow$ $m(1{)}^2+(m-1\left)\right(1)+2=0$

$\Rightarrow$ $m+m-1+2=0$

$\Rightarrow$ $2m+1=0$

$\Rightarrow$ $2m=-1$

$\therefore$ $m=\frac{-1}{2}$